Time Series Analysis of Corpus Christi Liquor Distribution


Jenna Ford, Christian Nava and Jonathan Tan
May 21, 2020

Variable Formatting


'data.frame':   375415 obs. of  6 variables:
 $ Customer_ID : int  701000317 701001770 701000317 701001770 701000317 701000317 701001770 701001770 701001770 701001770 ...
 $ Product     : Factor w/ 4017 levels "1800 ANEJO TEQ 6PK 750M",..: 2325 1211 2325 2325 2325 1972 1211 2325 2325 2325 ...
 $ Product_Type: Factor w/ 57 levels "ABSINTHE","AMARETTO",..: 49 29 49 49 49 54 29 49 49 49 ...
 $ STD_Cases   : num  377 361 330 307 280 231 217 192 192 190 ...
 $ Dollar_Sales: num  21987 69846 19246 17904 16498 ...
 $ date        : chr  "3/1/2017" "3/1/2018" "3/1/2018" "3/1/2018" ...

Products


[1] 57  2
Product_Type n
FLAVORED 69425
VODKA 48349
WHISKEY 33177
BOURBON 18838
BLENDS 18737
SILVER 18317
[1] 4017    2
Product n
TAAKA VODKA 80 PET 1.75L 2385
JACK DANIELS BLK WHSKY 1L 2269
TAAKA VODKA 80 1L 2183
CLAN MCGREGOR SCOTCH 1.75L 2091
RICH & RARE CANADIAN WHSKY 1.75L 2068
JACK DANIELS BLK WHSKY 1.75L 1994
[1] 34  2
Customer_ID n
700005448 37041
701001810 21316
701001907 19528
701001904 17879
701000317 17043
701001770 15558
[1] 4017    3
Product_Type Product n
VODKA TAAKA VODKA 80 PET 1.75L 2385
WHISKEY JACK DANIELS BLK WHSKY 1L 2269
VODKA TAAKA VODKA 80 1L 2183
SCOTCH CLAN MCGREGOR SCOTCH 1.75L 2091
BLENDS RICH & RARE CANADIAN WHSKY 1.75L 2068
WHISKEY JACK DANIELS BLK WHSKY 1.75L 1994
[1] 37391     4
Product_Type Product Customer_ID n
BLENDS CARSTAIRS BLEND 80 1L 700005925 84
BLENDS CARSTAIRS BLEND 80 1L 701000317 84
BLENDS CARSTAIRS BLEND 80 1L 701001790 84
BLENDS RICH & RARE CANADIAN WHSKY 1.75L 700005448 84
BLENDS RICH & RARE CANADIAN WHSKY 1.75L 700005850 84
BLENDS RICH & RARE CANADIAN WHSKY 1.75L 700005861 84

Put Combinations for Forecasting into a Dataframe and Choose 10 Sample Combinations


Product_Type Product Customer_ID
WHISKEY JACK DANIELS BLK WHSKY 750M 700005895
SILVER TORTILLA SILVER TEQ DSS 1.75L 700005448
GOLD FLOR DE CANA GOLD RUM 4YR 1L 701001904
TEQUILA CASA NOBLE CRYSTAL TEQ 6PK 750M 700005925
LIQUEUR PIRAS 51 CACHACA 80 1L 701001770
VODKA MCCORMICK VODKA 80 1.75L 701001908
VODKA MCCORMICK VODKA 80 TRVL 750M 700005926
BLENDS RICH & RARE CANADIAN RSV 6PK 750M 701001850
SILVER 1800 SILVER TEQ 750M 700005900
FLAVORED FIREBALL CINN WHSKY NL 1.75L 701001907

Time Series EDA & Forecasting


'data.frame':   840 obs. of  4 variables:
 $ date        : Factor w/ 84 levels "1/1/2013","1/1/2014",..: 1 29 36 43 50 57 64 71 78 8 ...
 $ Product_Type: Factor w/ 57 levels "ABSINTHE","AMARETTO",..: 53 53 53 53 53 53 53 53 53 53 ...
 $ Product     : Factor w/ 4017 levels "1800 ANEJO TEQ 6PK 750M",..: 1144 1144 1144 1144 1144 1144 1144 1144 1144 1144 ...
 $ Customer_ID : int  700005895 700005895 700005895 700005895 700005895 700005895 700005895 700005895 700005895 700005895 ...
'data.frame':   840 obs. of  6 variables:
 $ date        : chr  "1/1/2013" "2/1/2013" "3/1/2013" "4/1/2013" ...
 $ Product_Type: Factor w/ 57 levels "ABSINTHE","AMARETTO",..: 53 53 53 53 53 53 53 53 53 53 ...
 $ Product     : Factor w/ 4017 levels "1800 ANEJO TEQ 6PK 750M",..: 1144 1144 1144 1144 1144 1144 1144 1144 1144 1144 ...
 $ Customer_ID : int  700005895 700005895 700005895 700005895 700005895 700005895 700005895 700005895 700005895 700005895 ...
 $ STD_Cases   : num  3 0 1 5 0 0 0 4 0 0 ...
 $ Dollar_Sales: num  582 0 206 970 0 0 0 814 0 0 ...
# this code block is for individual product/customer combinations, no aggregation is done here

results <- data.frame(Product_Type=integer(),
                      Product=character(),
                      Customer=integer(),
                      ljung_10=double(),
                      ljung_24=double(),
                      ljung_results=character(),
                      top_5_bic=character(),
                      ADF=double(),
                      KPSS=double(),
                      stationarity_results=character(),
                      EqualMeans_1_ASE=double(),
                      EqualMeans_2_ASE=double(),
                      EqualMeans_3_ASE=double(),
                      EqualMeans_4_ASE=double(),
                      EqualMeans_5_ASE=double(),
                      EqualMeans_6_ASE=double(),
                      EqualMeans_7_ASE=double(),
                      EqualMeans_8_ASE=double(),
                      EqualMeans_9_ASE=double(),
                      EqualMeans_10_ASE=double(),
                      EqualMeans_11_ASE=double(),
                      EqualMeans_12_ASE=double(),
                      EqualMeans_F1=double(),
                      EqualMeans_F2=double(),
                      EqualMeans_F3=double(),
                      EqualMeans_F4=double(),
                      EqualMeans_F5=double(),
                      EqualMeans_F6=double(),
                      EqualMeans_F7=double(),
                      EqualMeans_F8=double(),
                      EqualMeans_F9=double(),
                      EqualMeans_F10=double(),
                      EqualMeans_F11=double(),
                      EqualMeans_F12=double(),
                      AR_1_ASE=double(),
                      AR_2_ASE=double(),
                      AR_3_ASE=double(),
                      AR_4_ASE=double(),
                      AR_5_ASE=double(),
                      AR_6_ASE=double(),
                      AR_7_ASE=double(),
                      AR_8_ASE=double(),
                      AR_9_ASE=double(),
                      AR_10_ASE=double(),
                      AR_11_ASE=double(),
                      AR_12_ASE=double(),
                      AR_F1=double(),
                      AR_F2=double(),
                      AR_F3=double(),
                      AR_F4=double(),
                      AR_F5=double(),
                      AR_F6=double(),
                      AR_F7=double(),
                      AR_F8=double(),
                      AR_F9=double(),
                      AR_F10=double(),
                      AR_F11=double(),
                      AR_F12=double(),
                      ARMA_1_ASE=double(),
                      ARMA_2_ASE=double(),
                      ARMA_3_ASE=double(),
                      ARMA_4_ASE=double(),
                      ARMA_5_ASE=double(),
                      ARMA_6_ASE=double(),
                      ARMA_7_ASE=double(),
                      ARMA_8_ASE=double(),
                      ARMA_9_ASE=double(),
                      ARMA_10_ASE=double(),
                      ARMA_11_ASE=double(),
                      ARMA_12_ASE=double(),
                      ARMA_F1=double(),
                      ARMA_F2=double(),
                      ARMA_F3=double(),
                      ARMA_F4=double(),
                      ARMA_F5=double(),
                      ARMA_F6=double(),
                      ARMA_F7=double(),
                      ARMA_F8=double(),
                      ARMA_F9=double(),
                      ARMA_F10=double(),
                      ARMA_F11=double(),
                      ARMA_F12=double(),
                      ARI_1_ASE=double(),
                      ARI_2_ASE=double(),
                      ARI_3_ASE=double(),
                      ARI_4_ASE=double(),
                      ARI_5_ASE=double(),
                      ARI_6_ASE=double(),
                      ARI_7_ASE=double(),
                      ARI_8_ASE=double(),
                      ARI_9_ASE=double(),
                      ARI_10_ASE=double(),
                      ARI_11_ASE=double(),
                      ARI_12_ASE=double(),
                      ARI_F1=double(),
                      ARI_F2=double(),
                      ARI_F3=double(),
                      ARI_F4=double(),
                      ARI_F5=double(),
                      ARI_F6=double(),
                      ARI_F7=double(),
                      ARI_F8=double(),
                      ARI_F9=double(),
                      ARI_F10=double(),
                      ARI_F11=double(),
                      ARI_F12=double(),
                      ARIMA_1_ASE=double(),
                      ARIMA_2_ASE=double(),
                      ARIMA_3_ASE=double(),
                      ARIMA_4_ASE=double(),
                      ARIMA_5_ASE=double(),
                      ARIMA_6_ASE=double(),
                      ARIMA_7_ASE=double(),
                      ARIMA_8_ASE=double(),
                      ARIMA_9_ASE=double(),
                      ARIMA_10_ASE=double(),
                      ARIMA_11_ASE=double(),
                      ARIMA_12_ASE=double(),
                      ARIMA_F1=double(),
                      ARIMA_F2=double(),
                      ARIMA_F3=double(),
                      ARIMA_F4=double(),
                      ARIMA_F5=double(),
                      ARIMA_F6=double(),
                      ARIMA_F7=double(),
                      ARIMA_F8=double(),
                      ARIMA_F9=double(),
                      ARIMA_F10=double(),
                      ARIMA_F11=double(),
                      ARIMA_F12=double(),
                      ARI_S12_1_ASE=double(),
                      ARI_S12_2_ASE=double(),
                      ARI_S12_3_ASE=double(),
                      ARI_S12_4_ASE=double(),
                      ARI_S12_5_ASE=double(),
                      ARI_S12_6_ASE=double(),
                      ARI_S12_7_ASE=double(),
                      ARI_S12_8_ASE=double(),
                      ARI_S12_9_ASE=double(),
                      ARI_S12_10_ASE=double(),
                      ARI_S12_11_ASE=double(),
                      ARI_S12_12_ASE=double(),
                      ARI_S12_F1=double(),
                      ARI_S12_F2=double(),
                      ARI_S12_F3=double(),
                      ARI_S12_F4=double(),
                      ARI_S12_F5=double(),
                      ARI_S12_F6=double(),
                      ARI_S12_F7=double(),
                      ARI_S12_F8=double(),
                      ARI_S12_F9=double(),
                      ARI_S12_F10=double(),
                      ARI_S12_F11=double(),
                      ARI_S12_F12=double(),
                      ARIMA_S12_1_ASE=double(),
                      ARIMA_S12_2_ASE=double(),
                      ARIMA_S12_3_ASE=double(),
                      ARIMA_S12_4_ASE=double(),
                      ARIMA_S12_5_ASE=double(),
                      ARIMA_S12_6_ASE=double(),
                      ARIMA_S12_7_ASE=double(),
                      ARIMA_S12_8_ASE=double(),
                      ARIMA_S12_9_ASE=double(),
                      ARIMA_S12_10_ASE=double(),
                      ARIMA_S12_11_ASE=double(),
                      ARIMA_S12_12_ASE=double(),
                      ARIMA_S12_F1=double(),
                      ARIMA_S12_F2=double(),
                      ARIMA_S12_F3=double(),
                      ARIMA_S12_F4=double(),
                      ARIMA_S12_F5=double(),
                      ARIMA_S12_F6=double(),
                      ARIMA_S12_F7=double(),
                      ARIMA_S12_F8=double(),
                      ARIMA_S12_F9=double(),
                      ARIMA_S12_F10=double(),
                      ARIMA_S12_F11=double(),
                      ARIMA_S12_F12=double(),
                      RF_1_ASE=double(),
                      RF_2_ASE=double(),
                      RF_3_ASE=double(),
                      RF_4_ASE=double(),
                      RF_5_ASE=double(),
                      RF_6_ASE=double(),
                      RF_7_ASE=double(),
                      RF_8_ASE=double(),
                      RF_9_ASE=double(),
                      RF_10_ASE=double(),
                      RF_11_ASE=double(),
                      RF_12_ASE=double(),
                      RF_F1=double(),
                      RF_F2=double(),
                      RF_F3=double(),
                      RF_F4=double(),
                      RF_F5=double(),
                      RF_F6=double(),
                      RF_F7=double(),
                      RF_F8=double(),
                      RF_F9=double(),
                      RF_F10=double(),
                      RF_F11=double(),
                      RF_F12=double(),
                      MLP_1_ASE=double(),
                      MLP_2_ASE=double(),
                      MLP_3_ASE=double(),
                      MLP_4_ASE=double(),
                      MLP_5_ASE=double(),
                      MLP_6_ASE=double(),
                      MLP_7_ASE=double(),
                      MLP_8_ASE=double(),
                      MLP_9_ASE=double(),
                      MLP_10_ASE=double(),
                      MLP_11_ASE=double(),
                      MLP_12_ASE=double(),
                      MLP_F1=double(),
                      MLP_F2=double(),
                      MLP_F3=double(),
                      MLP_F4=double(),
                      MLP_F5=double(),
                      MLP_F6=double(),
                      MLP_F7=double(),
                      MLP_F8=double(),
                      MLP_F9=double(),
                      MLP_F10=double(),
                      MLP_F11=double(),
                      MLP_F12=double(),
                      ACTUAL_1=double(),
                      ACTUAL_2=double(),
                      ACTUAL_3=double(),
                      ACTUAL_4=double(),
                      ACTUAL_5=double(),
                      ACTUAL_6=double(),
                      ACTUAL_7=double(),
                      ACTUAL_8=double(),
                      ACTUAL_9=double(),
                      ACTUAL_10=double(),
                      ACTUAL_11=double(),
                      ACTUAL_12=double(),
                      AR_F_Tally=double(),
                      AR_F_Conclusion=double(),
                      ARI_F_Tally=double(),
                      ARI_F_Conclusion=double(),
                      ARIS_F_Tally=double(),
                      ARIS_F_Conclusion=double(),
                      stringsAsFactors = FALSE)

# loop through sample combinations
for(i in 1:10) {
  sample_combinations1 = sample_combinations[i,]
  temp1 = inner_join(temp,sample_combinations1)
  product = sample_combinations1$Product
  customer = sample_combinations1$Customer_ID
  product_type = sample_combinations1$Customer_ID
  
  results[i,"Product_Type"] = product_type
  results[i,"Product"] = as.character(sample_combinations1$Product)
  results[i,"Customer"] = customer
  
  par(mfrow=c(1,1))
  plot.ts(temp1$STD_Cases, 
          main=c(paste("Standard Case Sales of ", product), 
                 paste("for Customer",customer)),
          xlab="Months",
          ylab="Standard Cases")
  
  par(mfrow = c(2,2))
  invisible(acf(temp1$STD_Cases, main="ACF"))
  invisible(parzen.wge(temp1$STD_Cases))

  invisible(acf(temp1$STD_Cases[0:length(temp1$date)/2], main="ACF for 1st Half of Series"))
  invisible(acf(temp1$STD_Cases[(1+length(temp1$date)/2):length(temp1$date)], main="ACF for 2nd Half of Series"))
  
  sink("file")
  ljung_10 = ljung.wge(temp1$STD_Cases,K=10)
  sink()
  cat("The Ljung-Box test with K=10 has a p-value of",ljung_10$pval,".")
  results[i,"ljung_10"] = ljung_10$pval
  
  sink("file")
  ljung_24 = ljung.wge(temp1$STD_Cases,K=24)
  sink()
  cat("The Ljung-Box test with K=24 has a p-value of",ljung_24$pval,".")
  results[i,"ljung_24"] = ljung_24$pval
  
  if (ljung_10$pval < .05 & ljung_24$pval < .05){
    print("Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise.")
    results[i,"ljung_results"] = "not white noise"
  } else if (ljung_10$pval > .05 & ljung_24$pval < .05){
    print("Ljung-Box test results: At a significance level of 0.05, the test is inconclusive.")
    results[i,"ljung_results"] = "inconclusive"
  } else if (ljung_10$pval < .05 & ljung_24$pval > .05){
    print("Ljung-Box test results: At a significance level of 0.05, the test is inconclusive.")
    results[i,"ljung_results"] = "inconclusive"
  } else {
    print("Ljung-Box test results: At a significance level of 0.05, we fail to reject the null hypothesis that this dataset is white noise.")
    results[i,"ljung_results"] = "white noise"
  }
  
  sink("file")
  aic = invisible(aic5.wge(temp1$STD_Cases,type="bic"))
  sink()
  
  for (row in 1:nrow(aic)) {
    if(aic[row,1] == 0 & aic[row,2] == 0){
      print("One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise.")
      results[i,"top_5_bic"] = "white noise"
    }
  }
  
  # Tests for stationarity
  
  # Augmented Dickey-Fuller
  adf=tseries::adf.test(temp1$STD_Cases)
  results[i,"ADF"] = adf$p.value
  
  # Kwiatkowski-Phillips-Schmidt-Shin
  kpss=tseries::kpss.test(temp1$STD_Cases)
  results[i,"KPSS"] = kpss$p.value
  
  if (adf$p.value < .05 &  kpss$p.value > .05){
    print("Both stationarity tests indicate this time series is stationary.")
    results[i,"stationarity_results"] = "stationary"
  } else if (adf$p.value >= .05 & kpss$p.value <= .05){
    print("Both stationarity tests indicate this time series is NOT stationary.")
    results[i,"stationarity_results"] = "not stationary"
  } else {
    print("Both tests for stationarity were inconclusive.")
    results[i,"stationarity_results"] = "inconclusive"
  }
  
  j=12
  
  #Equal Means Model
  
  trainingSize = 60
  ASEHolder1 = numeric()
  ASEHolder2 = numeric()
  ASEHolder3 = numeric()
  ASEHolder4 = numeric()
  ASEHolder5 = numeric()
  ASEHolder6 = numeric()
  ASEHolder7 = numeric()
  ASEHolder8 = numeric()
  ASEHolder9 = numeric()
  ASEHolder10 = numeric()
  ASEHolder11 = numeric()
  ASEHolder12 = numeric()

  for( k in 1:(84-(trainingSize + j) + 1))
  {
    sink("file")
    model0_mean = mean(temp1$STD_Cases[k:(k+(trainingSize-1))])
    ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - model0_mean)^2)
    ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - model0_mean)^2)
    ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - model0_mean)^2)
    ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - model0_mean)^2)
    ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - model0_mean)^2)
    ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - model0_mean)^2)
    ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - model0_mean)^2)
    ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - model0_mean)^2)
    ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - model0_mean)^2)
    ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - model0_mean)^2)
    ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - model0_mean)^2)
    ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - model0_mean)^2)
    sink()
    
    assign(paste("EqualMeans_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - model0_mean)^2)
    assign(paste("EqualMeans_DF_",k,sep=""),trainingSize-1)
  }
  
  WindowedASE1 = mean(ASEHolder1)
  WindowedASE2 = mean(ASEHolder2)
  WindowedASE3 = mean(ASEHolder3)
  WindowedASE4 = mean(ASEHolder4)
  WindowedASE5 = mean(ASEHolder5)
  WindowedASE6 = mean(ASEHolder6)
  WindowedASE7 = mean(ASEHolder7)
  WindowedASE8 = mean(ASEHolder8)
  WindowedASE9 = mean(ASEHolder9)
  WindowedASE10 = mean(ASEHolder10)
  WindowedASE11 = mean(ASEHolder11)
  WindowedASE12 = mean(ASEHolder12)
  results[i,paste0("EqualMeans_1_ASE")] = WindowedASE1
  results[i,paste0("EqualMeans_2_ASE")] = WindowedASE2
  results[i,paste0("EqualMeans_3_ASE")] = WindowedASE3
  results[i,paste0("EqualMeans_4_ASE")] = WindowedASE4
  results[i,paste0("EqualMeans_5_ASE")] = WindowedASE5
  results[i,paste0("EqualMeans_6_ASE")] = WindowedASE6
  results[i,paste0("EqualMeans_7_ASE")] = WindowedASE7
  results[i,paste0("EqualMeans_8_ASE")] = WindowedASE8
  results[i,paste0("EqualMeans_9_ASE")] = WindowedASE9
  results[i,paste0("EqualMeans_10_ASE")] = WindowedASE10
  results[i,paste0("EqualMeans_11_ASE")] = WindowedASE11
  results[i,paste0("EqualMeans_12_ASE")] = WindowedASE12
  results[i,paste0("EqualMeans_F1")] = model0_mean  
  results[i,paste0("EqualMeans_F2")] = model0_mean  
  results[i,paste0("EqualMeans_F3")] = model0_mean  
  results[i,paste0("EqualMeans_F4")] = model0_mean  
  results[i,paste0("EqualMeans_F5")] = model0_mean  
  results[i,paste0("EqualMeans_F6")] = model0_mean  
  results[i,paste0("EqualMeans_F7")] = model0_mean  
  results[i,paste0("EqualMeans_F8")] = model0_mean  
  results[i,paste0("EqualMeans_F9")] = model0_mean  
  results[i,paste0("EqualMeans_F10")] = model0_mean  
  results[i,paste0("EqualMeans_F11")] = model0_mean  
  results[i,paste0("EqualMeans_F12")] = model0_mean  

  #AR Model
  
  trainingSize = 60
  ASEHolder1 = numeric()
  ASEHolder2 = numeric()
  ASEHolder3 = numeric()
  ASEHolder4 = numeric()
  ASEHolder5 = numeric()
  ASEHolder6 = numeric()
  ASEHolder7 = numeric()
  ASEHolder8 = numeric()
  ASEHolder9 = numeric()
  ASEHolder10 = numeric()
  ASEHolder11 = numeric()
  ASEHolder12 = numeric()
  
  for( k in 1:(84-(trainingSize + j) + 1))
  {
    sink("file")
    model1 = invisible(aic.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],q=0,type="aic"))
    model1 = invisible(aic.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],q=0,type="aic"))
    if (model1$p == 0){
      newphi = 1
    } else {
      newphi = model1$p
    } 
    model1_est = invisible(est.ar.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],p=newphi))
    forecasts = fore.aruma.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],phi = model1_est$phi, theta = 0, s = 0, d = 0,n.ahead = j,plot=FALSE)

    ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - forecasts$f[1:1])^2)
    ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - forecasts$f[1:2])^2)
    ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - forecasts$f[1:3])^2)
    ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - forecasts$f[1:4])^2)
    ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - forecasts$f[1:5])^2)
    ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - forecasts$f[1:6])^2)
    ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - forecasts$f[1:7])^2)
    ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - forecasts$f[1:8])^2)
    ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - forecasts$f[1:9])^2)
    ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - forecasts$f[1:10])^2)
    ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - forecasts$f[1:11])^2)
    ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - forecasts$f[1:12])^2)
    sink()
    
    assign(paste("AR_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - forecasts$f)^2)
    assign(paste("AR_DF_",k,sep=""),trainingSize-(newphi+1))

  }
  
  WindowedASE1 = mean(ASEHolder1)
  WindowedASE2 = mean(ASEHolder2)
  WindowedASE3 = mean(ASEHolder3)
  WindowedASE4 = mean(ASEHolder4)
  WindowedASE5 = mean(ASEHolder5)
  WindowedASE6 = mean(ASEHolder6)
  WindowedASE7 = mean(ASEHolder7)
  WindowedASE8 = mean(ASEHolder8)
  WindowedASE9 = mean(ASEHolder9)
  WindowedASE10 = mean(ASEHolder10)
  WindowedASE11 = mean(ASEHolder11)
  WindowedASE12 = mean(ASEHolder12)
  results[i,paste0("AR_1_ASE")] = WindowedASE1
  results[i,paste0("AR_2_ASE")] = WindowedASE2
  results[i,paste0("AR_3_ASE")] = WindowedASE3
  results[i,paste0("AR_4_ASE")] = WindowedASE4
  results[i,paste0("AR_5_ASE")] = WindowedASE5
  results[i,paste0("AR_6_ASE")] = WindowedASE6
  results[i,paste0("AR_7_ASE")] = WindowedASE7
  results[i,paste0("AR_8_ASE")] = WindowedASE8
  results[i,paste0("AR_9_ASE")] = WindowedASE9
  results[i,paste0("AR_10_ASE")] = WindowedASE10
  results[i,paste0("AR_11_ASE")] = WindowedASE11
  results[i,paste0("AR_12_ASE")] = WindowedASE12
  results[i,paste0("AR_F1")] = forecasts$f[1]  
  results[i,paste0("AR_F2")] = forecasts$f[2]   
  results[i,paste0("AR_F3")] = forecasts$f[3]   
  results[i,paste0("AR_F4")] = forecasts$f[4]   
  results[i,paste0("AR_F5")] = forecasts$f[5]   
  results[i,paste0("AR_F6")] = forecasts$f[6]   
  results[i,paste0("AR_F7")] = forecasts$f[7]   
  results[i,paste0("AR_F8")] = forecasts$f[8]   
  results[i,paste0("AR_F9")] = forecasts$f[9]   
  results[i,paste0("AR_F10")] = forecasts$f[10]   
  results[i,paste0("AR_F11")] = forecasts$f[11]   
  results[i,paste0("AR_F12")] = forecasts$f[12]  

  
  #ARMA Model
  
  trainingSize = 60
  ASEHolder1 = numeric()
  ASEHolder2 = numeric()
  ASEHolder3 = numeric()
  ASEHolder4 = numeric()
  ASEHolder5 = numeric()
  ASEHolder6 = numeric()
  ASEHolder7 = numeric()
  ASEHolder8 = numeric()
  ASEHolder9 = numeric()
  ASEHolder10 = numeric()
  ASEHolder11 = numeric()
  ASEHolder12 = numeric()
  
  for( k in 1:(84-(trainingSize + j) + 1))
  {
    sink("file")
    model1 = invisible(aic.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],type="aic"))
    model1_est = invisible(est.arma.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],p=model1$p,q=model1$q))
    forecasts = fore.aruma.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],phi = model1_est$phi, theta = model1_est$theta, s = 0, d = 0,n.ahead = j,plot=FALSE)

    ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - forecasts$f[1:1])^2)
    ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - forecasts$f[1:2])^2)
    ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - forecasts$f[1:3])^2)
    ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - forecasts$f[1:4])^2)
    ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - forecasts$f[1:5])^2)
    ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - forecasts$f[1:6])^2)
    ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - forecasts$f[1:7])^2)
    ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - forecasts$f[1:8])^2)
    ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - forecasts$f[1:9])^2)
    ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - forecasts$f[1:10])^2)
    ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - forecasts$f[1:11])^2)
    ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - forecasts$f[1:12])^2)
    sink()
    
    assign(paste("ARMA_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - forecasts$f)^2)

  }
  
  WindowedASE1 = mean(ASEHolder1)
  WindowedASE2 = mean(ASEHolder2)
  WindowedASE3 = mean(ASEHolder3)
  WindowedASE4 = mean(ASEHolder4)
  WindowedASE5 = mean(ASEHolder5)
  WindowedASE6 = mean(ASEHolder6)
  WindowedASE7 = mean(ASEHolder7)
  WindowedASE8 = mean(ASEHolder8)
  WindowedASE9 = mean(ASEHolder9)
  WindowedASE10 = mean(ASEHolder10)
  WindowedASE11 = mean(ASEHolder11)
  WindowedASE12 = mean(ASEHolder12)
  results[i,paste0("ARMA_1_ASE")] = WindowedASE1
  results[i,paste0("ARMA_2_ASE")] = WindowedASE2
  results[i,paste0("ARMA_3_ASE")] = WindowedASE3
  results[i,paste0("ARMA_4_ASE")] = WindowedASE4
  results[i,paste0("ARMA_5_ASE")] = WindowedASE5
  results[i,paste0("ARMA_6_ASE")] = WindowedASE6
  results[i,paste0("ARMA_7_ASE")] = WindowedASE7
  results[i,paste0("ARMA_8_ASE")] = WindowedASE8
  results[i,paste0("ARMA_9_ASE")] = WindowedASE9
  results[i,paste0("ARMA_10_ASE")] = WindowedASE10
  results[i,paste0("ARMA_11_ASE")] = WindowedASE11
  results[i,paste0("ARMA_12_ASE")] = WindowedASE12
  results[i,paste0("ARMA_F1")] = forecasts$f[1]  
  results[i,paste0("ARMA_F2")] = forecasts$f[2]   
  results[i,paste0("ARMA_F3")] = forecasts$f[3]   
  results[i,paste0("ARMA_F4")] = forecasts$f[4]   
  results[i,paste0("ARMA_F5")] = forecasts$f[5]   
  results[i,paste0("ARMA_F6")] = forecasts$f[6]   
  results[i,paste0("ARMA_F7")] = forecasts$f[7]   
  results[i,paste0("ARMA_F8")] = forecasts$f[8]   
  results[i,paste0("ARMA_F9")] = forecasts$f[9]   
  results[i,paste0("ARMA_F10")] = forecasts$f[10]   
  results[i,paste0("ARMA_F11")] = forecasts$f[11]   
  results[i,paste0("ARMA_F12")] = forecasts$f[12]  

  
  
  #ARIMA Model with q=0 and d=1
  nulldev()
  temp2 = artrans.wge(temp1$STD_Cases,1)
  dev.off()
  
  trainingSize = 60
  ASEHolder1 = numeric()
  ASEHolder2 = numeric()
  ASEHolder3 = numeric()
  ASEHolder4 = numeric()
  ASEHolder5 = numeric()
  ASEHolder6 = numeric()
  ASEHolder7 = numeric()
  ASEHolder8 = numeric()
  ASEHolder9 = numeric()
  ASEHolder10 = numeric()
  ASEHolder11 = numeric()
  ASEHolder12 = numeric()
    
  for( k in 1:(84-(trainingSize + j) + 1))
  {
    sink("file")
    model1 = invisible(aic.wge(temp2[k:(k+(trainingSize-1-1))],q=0,type="aic"))
    model1_est = invisible(est.ar.wge(temp2[k:(k+(trainingSize-1-1))],p=model1$p))
    forecasts = fore.aruma.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],phi = model1_est$phi, theta = 0, s = 0, d = 1,n.ahead = j,plot=FALSE)
    ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - forecasts$f[1:1])^2)
    ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - forecasts$f[1:2])^2)
    ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - forecasts$f[1:3])^2)
    ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - forecasts$f[1:4])^2)
    ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - forecasts$f[1:5])^2)
    ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - forecasts$f[1:6])^2)
    ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - forecasts$f[1:7])^2)
    ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - forecasts$f[1:8])^2)
    ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - forecasts$f[1:9])^2)
    ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - forecasts$f[1:10])^2)
    ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - forecasts$f[1:11])^2)
    ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - forecasts$f[1:12])^2)
    sink()
    
    assign(paste("ARI_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - forecasts$f)^2)
    assign(paste("ARI_DF_",k,sep=""),trainingSize-(model1$p+1))

  }
  
  WindowedASE1 = mean(ASEHolder1)
  WindowedASE2 = mean(ASEHolder2)
  WindowedASE3 = mean(ASEHolder3)
  WindowedASE4 = mean(ASEHolder4)
  WindowedASE5 = mean(ASEHolder5)
  WindowedASE6 = mean(ASEHolder6)
  WindowedASE7 = mean(ASEHolder7)
  WindowedASE8 = mean(ASEHolder8)
  WindowedASE9 = mean(ASEHolder9)
  WindowedASE10 = mean(ASEHolder10)
  WindowedASE11 = mean(ASEHolder11)
  WindowedASE12 = mean(ASEHolder12)
  results[i,paste0("ARI_1_ASE")] = WindowedASE1
  results[i,paste0("ARI_2_ASE")] = WindowedASE2
  results[i,paste0("ARI_3_ASE")] = WindowedASE3
  results[i,paste0("ARI_4_ASE")] = WindowedASE4
  results[i,paste0("ARI_5_ASE")] = WindowedASE5
  results[i,paste0("ARI_6_ASE")] = WindowedASE6
  results[i,paste0("ARI_7_ASE")] = WindowedASE7
  results[i,paste0("ARI_8_ASE")] = WindowedASE8
  results[i,paste0("ARI_9_ASE")] = WindowedASE9
  results[i,paste0("ARI_10_ASE")] = WindowedASE10
  results[i,paste0("ARI_11_ASE")] = WindowedASE11
  results[i,paste0("ARI_12_ASE")] = WindowedASE12
  results[i,paste0("ARI_F1")] = forecasts$f[1]  
  results[i,paste0("ARI_F2")] = forecasts$f[2]   
  results[i,paste0("ARI_F3")] = forecasts$f[3]   
  results[i,paste0("ARI_F4")] = forecasts$f[4]   
  results[i,paste0("ARI_F5")] = forecasts$f[5]   
  results[i,paste0("ARI_F6")] = forecasts$f[6]   
  results[i,paste0("ARI_F7")] = forecasts$f[7]   
  results[i,paste0("ARI_F8")] = forecasts$f[8]   
  results[i,paste0("ARI_F9")] = forecasts$f[9]   
  results[i,paste0("ARI_F10")] = forecasts$f[10]   
  results[i,paste0("ARI_F11")] = forecasts$f[11]   
  results[i,paste0("ARI_F12")] = forecasts$f[12]

  
  #ARIMA Model with d=1
  nulldev()
  temp2 = artrans.wge(temp1$STD_Cases,1)
  dev.off()
  
  trainingSize = 60
  ASEHolder1 = numeric()
  ASEHolder2 = numeric()
  ASEHolder3 = numeric()
  ASEHolder4 = numeric()
  ASEHolder5 = numeric()
  ASEHolder6 = numeric()
  ASEHolder7 = numeric()
  ASEHolder8 = numeric()
  ASEHolder9 = numeric()
  ASEHolder10 = numeric()
  ASEHolder11 = numeric()
  ASEHolder12 = numeric()
    
  for( k in 1:(84-(trainingSize + j) + 1))
  {
    sink("file")
    model1 = invisible(aic.wge(temp2[k:(k+(trainingSize-1-1))],type="aic"))
    model1_est = invisible(est.arma.wge(temp2[k:(k+(trainingSize-1-1))],p=model1$p,q=model1$q))
    forecasts = fore.aruma.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],phi = model1_est$phi, theta = model1_est$theta, s = 0, d = 1,n.ahead = j,plot=FALSE)
    ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - forecasts$f[1:1])^2)
    ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - forecasts$f[1:2])^2)
    ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - forecasts$f[1:3])^2)
    ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - forecasts$f[1:4])^2)
    ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - forecasts$f[1:5])^2)
    ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - forecasts$f[1:6])^2)
    ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - forecasts$f[1:7])^2)
    ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - forecasts$f[1:8])^2)
    ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - forecasts$f[1:9])^2)
    ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - forecasts$f[1:10])^2)
    ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - forecasts$f[1:11])^2)
    ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - forecasts$f[1:12])^2)
    sink()
    
    assign(paste("ARIMA_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - forecasts$f)^2)

  }
  
  WindowedASE1 = mean(ASEHolder1)
  WindowedASE2 = mean(ASEHolder2)
  WindowedASE3 = mean(ASEHolder3)
  WindowedASE4 = mean(ASEHolder4)
  WindowedASE5 = mean(ASEHolder5)
  WindowedASE6 = mean(ASEHolder6)
  WindowedASE7 = mean(ASEHolder7)
  WindowedASE8 = mean(ASEHolder8)
  WindowedASE9 = mean(ASEHolder9)
  WindowedASE10 = mean(ASEHolder10)
  WindowedASE11 = mean(ASEHolder11)
  WindowedASE12 = mean(ASEHolder12)
  results[i,paste0("ARIMA_1_ASE")] = WindowedASE1
  results[i,paste0("ARIMA_2_ASE")] = WindowedASE2
  results[i,paste0("ARIMA_3_ASE")] = WindowedASE3
  results[i,paste0("ARIMA_4_ASE")] = WindowedASE4
  results[i,paste0("ARIMA_5_ASE")] = WindowedASE5
  results[i,paste0("ARIMA_6_ASE")] = WindowedASE6
  results[i,paste0("ARIMA_7_ASE")] = WindowedASE7
  results[i,paste0("ARIMA_8_ASE")] = WindowedASE8
  results[i,paste0("ARIMA_9_ASE")] = WindowedASE9
  results[i,paste0("ARIMA_10_ASE")] = WindowedASE10
  results[i,paste0("ARIMA_11_ASE")] = WindowedASE11
  results[i,paste0("ARIMA_12_ASE")] = WindowedASE12
  results[i,paste0("ARIMA_F1")] = forecasts$f[1]  
  results[i,paste0("ARIMA_F2")] = forecasts$f[2]   
  results[i,paste0("ARIMA_F3")] = forecasts$f[3]   
  results[i,paste0("ARIMA_F4")] = forecasts$f[4]   
  results[i,paste0("ARIMA_F5")] = forecasts$f[5]   
  results[i,paste0("ARIMA_F6")] = forecasts$f[6]   
  results[i,paste0("ARIMA_F7")] = forecasts$f[7]   
  results[i,paste0("ARIMA_F8")] = forecasts$f[8]   
  results[i,paste0("ARIMA_F9")] = forecasts$f[9]   
  results[i,paste0("ARIMA_F10")] = forecasts$f[10]   
  results[i,paste0("ARIMA_F11")] = forecasts$f[11]   
  results[i,paste0("ARIMA_F12")] = forecasts$f[12]

  
 
#ARIMA Model with q=0 and S=12
  nulldev()
  temp2 = artrans.wge(temp1$STD_Cases,phi.tr=c(rep(0,11),1))
  dev.off()
  
  trainingSize = 60
  ASEHolder1 = numeric()
  ASEHolder2 = numeric()
  ASEHolder3 = numeric()
  ASEHolder4 = numeric()
  ASEHolder5 = numeric()
  ASEHolder6 = numeric()
  ASEHolder7 = numeric()
  ASEHolder8 = numeric()
  ASEHolder9 = numeric()
  ASEHolder10 = numeric()
  ASEHolder11 = numeric()
  ASEHolder12 = numeric()
  
  for( k in 1:(84-(trainingSize + j) + 1))
  {
    sink("file")
    model1 = invisible(aic.wge(temp2[k:(k+(trainingSize-1-12))],q=0, type="aic"))
    if (model1$p == 0){
      newphi = 1
    } else {
      newphi = model1$p
    } 
    model1_est = invisible(est.ar.wge(temp2[k:(k+(trainingSize-1-12))],p=newphi))
    forecasts = fore.aruma.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],phi = model1_est$phi, theta = 0, s = 12, d = 0,n.ahead = j,plot=FALSE)
    ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - forecasts$f[1:1])^2)
    ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - forecasts$f[1:2])^2)
    ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - forecasts$f[1:3])^2)
    ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - forecasts$f[1:4])^2)
    ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - forecasts$f[1:5])^2)
    ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - forecasts$f[1:6])^2)
    ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - forecasts$f[1:7])^2)
    ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - forecasts$f[1:8])^2)
    ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - forecasts$f[1:9])^2)
    ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - forecasts$f[1:10])^2)
    ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - forecasts$f[1:11])^2)
    ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - forecasts$f[1:12])^2)
    sink()
    
    assign(paste("ARIS_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - forecasts$f)^2)
    assign(paste("ARIS_DF_",k,sep=""),trainingSize-(newphi+1))

  }
  
  WindowedASE1 = mean(ASEHolder1)
  WindowedASE2 = mean(ASEHolder2)
  WindowedASE3 = mean(ASEHolder3)
  WindowedASE4 = mean(ASEHolder4)
  WindowedASE5 = mean(ASEHolder5)
  WindowedASE6 = mean(ASEHolder6)
  WindowedASE7 = mean(ASEHolder7)
  WindowedASE8 = mean(ASEHolder8)
  WindowedASE9 = mean(ASEHolder9)
  WindowedASE10 = mean(ASEHolder10)
  WindowedASE11 = mean(ASEHolder11)
  WindowedASE12 = mean(ASEHolder12)
  results[i,paste0("ARI_S12_1_ASE")] = WindowedASE1
  results[i,paste0("ARI_S12_2_ASE")] = WindowedASE2
  results[i,paste0("ARI_S12_3_ASE")] = WindowedASE3
  results[i,paste0("ARI_S12_4_ASE")] = WindowedASE4
  results[i,paste0("ARI_S12_5_ASE")] = WindowedASE5
  results[i,paste0("ARI_S12_6_ASE")] = WindowedASE6
  results[i,paste0("ARI_S12_7_ASE")] = WindowedASE7
  results[i,paste0("ARI_S12_8_ASE")] = WindowedASE8
  results[i,paste0("ARI_S12_9_ASE")] = WindowedASE9
  results[i,paste0("ARI_S12_10_ASE")] = WindowedASE10
  results[i,paste0("ARI_S12_11_ASE")] = WindowedASE11
  results[i,paste0("ARI_S12_12_ASE")] = WindowedASE12
  results[i,paste0("ARI_S12_F1")] = forecasts$f[1]  
  results[i,paste0("ARI_S12_F2")] = forecasts$f[2]   
  results[i,paste0("ARI_S12_F3")] = forecasts$f[3]   
  results[i,paste0("ARI_S12_F4")] = forecasts$f[4]   
  results[i,paste0("ARI_S12_F5")] = forecasts$f[5]   
  results[i,paste0("ARI_S12_F6")] = forecasts$f[6]   
  results[i,paste0("ARI_S12_F7")] = forecasts$f[7]   
  results[i,paste0("ARI_S12_F8")] = forecasts$f[8]   
  results[i,paste0("ARI_S12_F9")] = forecasts$f[9]   
  results[i,paste0("ARI_S12_F10")] = forecasts$f[10]   
  results[i,paste0("ARI_S12_F11")] = forecasts$f[11]   
  results[i,paste0("ARI_S12_F12")] = forecasts$f[12]   

  
  
  #ARIMA Model with S=12
  nulldev()
  temp2 = artrans.wge(temp1$STD_Cases,phi.tr=c(rep(0,11),1))
  dev.off()
  
  trainingSize = 60
  ASEHolder1 = numeric()
  ASEHolder2 = numeric()
  ASEHolder3 = numeric()
  ASEHolder4 = numeric()
  ASEHolder5 = numeric()
  ASEHolder6 = numeric()
  ASEHolder7 = numeric()
  ASEHolder8 = numeric()
  ASEHolder9 = numeric()
  ASEHolder10 = numeric()
  ASEHolder11 = numeric()
  ASEHolder12 = numeric()
  
  for( k in 1:(84-(trainingSize + j) + 1))
  {
    sink("file")
    model1 = invisible(aic.wge(temp2[k:(k+(trainingSize-1-12))],type="aic"))
    model1_est = invisible(est.arma.wge(temp2[k:(k+(trainingSize-1-12))],p=model1$p,q=model1$q))
    forecasts = fore.aruma.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],phi = model1_est$phi, theta = model1_est$theta, s = 12, d = 0,n.ahead = j,plot=FALSE)
    ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - forecasts$f[1:1])^2)
    ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - forecasts$f[1:2])^2)
    ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - forecasts$f[1:3])^2)
    ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - forecasts$f[1:4])^2)
    ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - forecasts$f[1:5])^2)
    ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - forecasts$f[1:6])^2)
    ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - forecasts$f[1:7])^2)
    ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - forecasts$f[1:8])^2)
    ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - forecasts$f[1:9])^2)
    ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - forecasts$f[1:10])^2)
    ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - forecasts$f[1:11])^2)
    ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - forecasts$f[1:12])^2)
    sink()
    
    assign(paste("ARIMAS_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - forecasts$f)^2)

  }
  
  WindowedASE1 = mean(ASEHolder1)
  WindowedASE2 = mean(ASEHolder2)
  WindowedASE3 = mean(ASEHolder3)
  WindowedASE4 = mean(ASEHolder4)
  WindowedASE5 = mean(ASEHolder5)
  WindowedASE6 = mean(ASEHolder6)
  WindowedASE7 = mean(ASEHolder7)
  WindowedASE8 = mean(ASEHolder8)
  WindowedASE9 = mean(ASEHolder9)
  WindowedASE10 = mean(ASEHolder10)
  WindowedASE11 = mean(ASEHolder11)
  WindowedASE12 = mean(ASEHolder12)
  results[i,paste0("ARIMA_S12_1_ASE")] = WindowedASE1
  results[i,paste0("ARIMA_S12_2_ASE")] = WindowedASE2
  results[i,paste0("ARIMA_S12_3_ASE")] = WindowedASE3
  results[i,paste0("ARIMA_S12_4_ASE")] = WindowedASE4
  results[i,paste0("ARIMA_S12_5_ASE")] = WindowedASE5
  results[i,paste0("ARIMA_S12_6_ASE")] = WindowedASE6
  results[i,paste0("ARIMA_S12_7_ASE")] = WindowedASE7
  results[i,paste0("ARIMA_S12_8_ASE")] = WindowedASE8
  results[i,paste0("ARIMA_S12_9_ASE")] = WindowedASE9
  results[i,paste0("ARIMA_S12_10_ASE")] = WindowedASE10
  results[i,paste0("ARIMA_S12_11_ASE")] = WindowedASE11
  results[i,paste0("ARIMA_S12_12_ASE")] = WindowedASE12
  results[i,paste0("ARIMA_S12_F1")] = forecasts$f[1]  
  results[i,paste0("ARIMA_S12_F2")] = forecasts$f[2]   
  results[i,paste0("ARIMA_S12_F3")] = forecasts$f[3]   
  results[i,paste0("ARIMA_S12_F4")] = forecasts$f[4]   
  results[i,paste0("ARIMA_S12_F5")] = forecasts$f[5]   
  results[i,paste0("ARIMA_S12_F6")] = forecasts$f[6]   
  results[i,paste0("ARIMA_S12_F7")] = forecasts$f[7]   
  results[i,paste0("ARIMA_S12_F8")] = forecasts$f[8]   
  results[i,paste0("ARIMA_S12_F9")] = forecasts$f[9]   
  results[i,paste0("ARIMA_S12_F10")] = forecasts$f[10]   
  results[i,paste0("ARIMA_S12_F11")] = forecasts$f[11]   
  results[i,paste0("ARIMA_S12_F12")] = forecasts$f[12]   

  
  
  #Random Forest
  trainingSize = 60
  ASEHolder1 = numeric()
  ASEHolder2 = numeric()
  ASEHolder3 = numeric()
  ASEHolder4 = numeric()
  ASEHolder5 = numeric()
  ASEHolder6 = numeric()
  ASEHolder7 = numeric()
  ASEHolder8 = numeric()
  ASEHolder9 = numeric()
  ASEHolder10 = numeric()
  ASEHolder11 = numeric()
  ASEHolder12 = numeric()
  
  for( k in 1:(84-(trainingSize + j) + 1))
  {
    sink("file")
   
    forecasts <- rf_ts(j, temp1[k:(k+(trainingSize-1)),], FALSE)
    
    ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - forecasts$forecast[1:1])^2)
    ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - forecasts$forecast[1:2])^2)
    ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - forecasts$forecast[1:3])^2)
    ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - forecasts$forecast[1:4])^2)
    ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - forecasts$forecast[1:5])^2)
    ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - forecasts$forecast[1:6])^2)
    ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - forecasts$forecast[1:7])^2)
    ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - forecasts$forecast[1:8])^2)
    ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - forecasts$forecast[1:9])^2)
    ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - forecasts$forecast[1:10])^2)
    ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - forecasts$forecast[1:11])^2)
    ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - forecasts$forecast[1:12])^2)
    sink()
    
    assign(paste("RF_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - forecasts$forecast)^2)

  }
  
  WindowedASE1 = mean(ASEHolder1)
  WindowedASE2 = mean(ASEHolder2)
  WindowedASE3 = mean(ASEHolder3)
  WindowedASE4 = mean(ASEHolder4)
  WindowedASE5 = mean(ASEHolder5)
  WindowedASE6 = mean(ASEHolder6)
  WindowedASE7 = mean(ASEHolder7)
  WindowedASE8 = mean(ASEHolder8)
  WindowedASE9 = mean(ASEHolder9)
  WindowedASE10 = mean(ASEHolder10)
  WindowedASE11 = mean(ASEHolder11)
  WindowedASE12 = mean(ASEHolder12)
  results[i,paste0("RF_1_ASE")] = WindowedASE1
  results[i,paste0("RF_2_ASE")] = WindowedASE2
  results[i,paste0("RF_3_ASE")] = WindowedASE3
  results[i,paste0("RF_4_ASE")] = WindowedASE4
  results[i,paste0("RF_5_ASE")] = WindowedASE5
  results[i,paste0("RF_6_ASE")] = WindowedASE6
  results[i,paste0("RF_7_ASE")] = WindowedASE7
  results[i,paste0("RF_8_ASE")] = WindowedASE8
  results[i,paste0("RF_9_ASE")] = WindowedASE9
  results[i,paste0("RF_10_ASE")] = WindowedASE10
  results[i,paste0("RF_11_ASE")] = WindowedASE11
  results[i,paste0("RF_12_ASE")] = WindowedASE12
  results[i,paste0("RF_F1")] = forecasts$forecast[1]  
  results[i,paste0("RF_F2")] = forecasts$forecast[2]   
  results[i,paste0("RF_F3")] = forecasts$forecast[3]   
  results[i,paste0("RF_F4")] = forecasts$forecast[4]   
  results[i,paste0("RF_F5")] = forecasts$forecast[5]   
  results[i,paste0("RF_F6")] = forecasts$forecast[6]   
  results[i,paste0("RF_F7")] = forecasts$forecast[7]   
  results[i,paste0("RF_F8")] = forecasts$forecast[8]   
  results[i,paste0("RF_F9")] = forecasts$forecast[9]   
  results[i,paste0("RF_F10")] = forecasts$forecast[10]   
  results[i,paste0("RF_F11")] = forecasts$forecast[11]   
  results[i,paste0("RF_F12")] = forecasts$forecast[12]   

  
  
  # MLP
  trainingSize = 60
  ASEHolder1 = numeric()
  ASEHolder2 = numeric()
  ASEHolder3 = numeric()
  ASEHolder4 = numeric()
  ASEHolder5 = numeric()
  ASEHolder6 = numeric()
  ASEHolder7 = numeric()
  ASEHolder8 = numeric()
  ASEHolder9 = numeric()
  ASEHolder10 = numeric()
  ASEHolder11 = numeric()
  ASEHolder12 = numeric()
  
  for( k in 1:(84-(trainingSize + j) + 1))
  {
    sink("file")

    forecasts <- nnc(temp1$STD_Cases[k:(k+(trainingSize-1))], j, 10, c(5, 10, 15, 5), FALSE)
    
    ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - forecasts$forecast[1:1])^2)
    ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - forecasts$forecast[1:2])^2)
    ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - forecasts$forecast[1:3])^2)
    ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - forecasts$forecast[1:4])^2)
    ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - forecasts$forecast[1:5])^2)
    ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - forecasts$forecast[1:6])^2)
    ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - forecasts$forecast[1:7])^2)
    ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - forecasts$forecast[1:8])^2)
    ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - forecasts$forecast[1:9])^2)
    ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - forecasts$forecast[1:10])^2)
    ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - forecasts$forecast[1:11])^2)
    ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - forecasts$forecast[1:12])^2)
    sink()
    
    assign(paste("MLP_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - forecasts$forecast)^2)

  }
  
  WindowedASE1 = mean(ASEHolder1)
  WindowedASE2 = mean(ASEHolder2)
  WindowedASE3 = mean(ASEHolder3)
  WindowedASE4 = mean(ASEHolder4)
  WindowedASE5 = mean(ASEHolder5)
  WindowedASE6 = mean(ASEHolder6)
  WindowedASE7 = mean(ASEHolder7)
  WindowedASE8 = mean(ASEHolder8)
  WindowedASE9 = mean(ASEHolder9)
  WindowedASE10 = mean(ASEHolder10)
  WindowedASE11 = mean(ASEHolder11)
  WindowedASE12 = mean(ASEHolder12)
  results[i,paste0("MLP_1_ASE")] = WindowedASE1
  results[i,paste0("MLP_2_ASE")] = WindowedASE2
  results[i,paste0("MLP_3_ASE")] = WindowedASE3
  results[i,paste0("MLP_4_ASE")] = WindowedASE4
  results[i,paste0("MLP_5_ASE")] = WindowedASE5
  results[i,paste0("MLP_6_ASE")] = WindowedASE6
  results[i,paste0("MLP_7_ASE")] = WindowedASE7
  results[i,paste0("MLP_8_ASE")] = WindowedASE8
  results[i,paste0("MLP_9_ASE")] = WindowedASE9
  results[i,paste0("MLP_10_ASE")] = WindowedASE10
  results[i,paste0("MLP_11_ASE")] = WindowedASE11
  results[i,paste0("MLP_12_ASE")] = WindowedASE12
  results[i,paste0("MLP_F1")] = forecasts$forecast[1]  
  results[i,paste0("MLP_F2")] = forecasts$forecast[2]   
  results[i,paste0("MLP_F3")] = forecasts$forecast[3]   
  results[i,paste0("MLP_F4")] = forecasts$forecast[4]   
  results[i,paste0("MLP_F5")] = forecasts$forecast[5]   
  results[i,paste0("MLP_F6")] = forecasts$forecast[6]   
  results[i,paste0("MLP_F7")] = forecasts$forecast[7]   
  results[i,paste0("MLP_F8")] = forecasts$forecast[8]   
  results[i,paste0("MLP_F9")] = forecasts$forecast[9]   
  results[i,paste0("MLP_F10")] = forecasts$forecast[10]   
  results[i,paste0("MLP_F11")] = forecasts$forecast[11]   
  results[i,paste0("MLP_F12")] = forecasts$forecast[12]   

  
  results[i,paste0("ACTUAL_1")] = temp1$STD_Cases[73]
  results[i,paste0("ACTUAL_2")] = temp1$STD_Cases[74]
  results[i,paste0("ACTUAL_3")] = temp1$STD_Cases[75]
  results[i,paste0("ACTUAL_4")] = temp1$STD_Cases[76]
  results[i,paste0("ACTUAL_5")] = temp1$STD_Cases[77]
  results[i,paste0("ACTUAL_6")] = temp1$STD_Cases[78]
  results[i,paste0("ACTUAL_7")] = temp1$STD_Cases[79]
  results[i,paste0("ACTUAL_8")] = temp1$STD_Cases[80]
  results[i,paste0("ACTUAL_9")] = temp1$STD_Cases[81]
  results[i,paste0("ACTUAL_10")] = temp1$STD_Cases[82]
  results[i,paste0("ACTUAL_11")] = temp1$STD_Cases[83]
  results[i,paste0("ACTUAL_12")] = temp1$STD_Cases[84]

  
  #graph ASEs for each Model
  EqualMeans_Results <- rbind(EqualMeans_Results_1,EqualMeans_Results_2,EqualMeans_Results_3,EqualMeans_Results_4,EqualMeans_Results_5,EqualMeans_Results_6,
                              EqualMeans_Results_7,EqualMeans_Results_8,EqualMeans_Results_9,EqualMeans_Results_10,EqualMeans_Results_11,EqualMeans_Results_12,
                              EqualMeans_Results_13)
  
  AR_Results <- rbind(AR_Results_1,AR_Results_2,AR_Results_3,AR_Results_4,AR_Results_5,AR_Results_6,AR_Results_7,AR_Results_8,AR_Results_9,AR_Results_10,
                      AR_Results_11,AR_Results_12,AR_Results_13)
  
  ARMA_Results <- rbind(ARMA_Results_1,ARMA_Results_2,ARMA_Results_3,ARMA_Results_4,ARMA_Results_5,ARMA_Results_6,ARMA_Results_7,ARMA_Results_8,
                       ARMA_Results_9,ARMA_Results_10,ARMA_Results_11,ARMA_Results_12,ARMA_Results_13)

  ARI_Results <- rbind(ARI_Results_1,ARI_Results_2,ARI_Results_3,ARI_Results_4,ARI_Results_5,ARI_Results_6,ARI_Results_7,ARI_Results_8,
                         ARI_Results_9,ARI_Results_10,ARI_Results_11,ARI_Results_12,ARI_Results_13)
 
  ARIMA_Results <- rbind(ARIMA_Results_1,ARIMA_Results_2,ARIMA_Results_3,ARIMA_Results_4,ARIMA_Results_5,ARIMA_Results_6,ARIMA_Results_7,ARIMA_Results_8,
                         ARIMA_Results_9,ARIMA_Results_10,ARIMA_Results_11,ARIMA_Results_12,ARIMA_Results_13)
      
  ARIS_Results <- rbind(ARIS_Results_1,ARIS_Results_2,ARIS_Results_3,ARIS_Results_4,ARIS_Results_5,ARIS_Results_6,ARIS_Results_7,ARIS_Results_8,
                          ARIS_Results_9,ARIS_Results_10,ARIS_Results_11,ARIS_Results_12,ARIS_Results_13)
  
  ARIMAS_Results <- rbind(ARIMAS_Results_1,ARIMAS_Results_2,ARIMAS_Results_3,ARIMAS_Results_4,ARIMAS_Results_5,ARIMAS_Results_6,ARIMAS_Results_7,ARIMAS_Results_8,
                          ARIMAS_Results_9,ARIMAS_Results_10,ARIMAS_Results_11,ARIMAS_Results_12,ARIMAS_Results_13)
  
  RF_Results <- rbind(RF_Results_1,RF_Results_2,RF_Results_3,RF_Results_4,RF_Results_5,RF_Results_6,RF_Results_7,RF_Results_8,
                        RF_Results_9,RF_Results_10,RF_Results_11,RF_Results_12,RF_Results_13)
    
  MLP_Results <- rbind(MLP_Results_1,MLP_Results_2,MLP_Results_3,MLP_Results_4,MLP_Results_5,MLP_Results_6,MLP_Results_7,MLP_Results_8,
                      MLP_Results_9,MLP_Results_10,MLP_Results_11,MLP_Results_12,MLP_Results_13)
      
  EqualMeans_Means <- colMeans(EqualMeans_Results)
  AR_Means <- colMeans(AR_Results)
  ARMA_Means <- colMeans(ARMA_Results)
  ARI_Means <- colMeans(ARI_Results)
  ARIMA_Means <- colMeans(ARIMA_Results)
  ARIS_Means <- colMeans(ARIS_Results)
  ARIMAS_Means <- colMeans(ARIMAS_Results)
  RF_Means <- colMeans(RF_Results)
  MLP_Means <- colMeans(MLP_Results)
  Combined_Means <- data.frame(EqualMeans_Means,AR_Means, ARMA_Means, ARI_Means, ARIMA_Means, ARIS_Means, ARIMAS_Means,RF_Means,MLP_Means)
  Combined_Means$horizon <- as.numeric(row.names(Combined_Means))
  
# more colors #73EBAE
  g <- ggplot(data=Combined_Means, aes(horizon)) +
    geom_line(aes(y=EqualMeans_Means, color="Equal Means"),size=1.5) +
    geom_line(aes(y=AR_Means, color="AR"),size=1.5) +
    geom_line(aes(y=ARMA_Means, color="ARMA"),size=1.5) +
    geom_line(aes(y=ARI_Means, color="AR with d=1"),size=1.5) +
    geom_line(aes(y=ARIMA_Means, color="ARIMA with d=1"),size=1.5) +
    geom_line(aes(y=ARIS_Means, color="AR with s=12"),size=1.5) +
    geom_line(aes(y=ARIMAS_Means, color="ARIMA with d=0, s=12"),size=1.5) +
    geom_line(aes(y=RF_Means, color="Random Forest"),size=1.5) +
    geom_line(aes(y=MLP_Means, color="MLP"),size=1.5) +
    scale_color_manual(values = c(
      'Equal Means' = '#004159',
      'AR' = '#65A8C4',
      'ARMA' = '#8C65D3',
      'AR with d=1' = '#9A93EC',
      'ARIMA with d=1' = '#0052A5',
      'AR with s=12' = '#413BF7',
      'ARIMA with d=0, s=12' = '#00ADCE',
      'Random Forest' = '#59DBF1',
      'MLP' = '#00C590'
    )) +
    labs(color='Models') +
    scale_x_continuous(breaks=seq(0,13,1)) +
    ggtitle(paste("Model ASEs for ", product,"and Customer",customer)) +
    xlab("Month Ahead Forecast") +
    ylab("ASE") +
    theme(panel.background = element_blank(), axis.line = element_line(colour = "black"), legend.title = element_blank())
  
  print(g)
  
# f-statistic calculations
    EqualMeans_DF <- rbind(EqualMeans_DF_1,EqualMeans_DF_2,EqualMeans_DF_3,EqualMeans_DF_4,EqualMeans_DF_5,EqualMeans_DF_6,EqualMeans_DF_7,
                           EqualMeans_DF_8,EqualMeans_DF_9,EqualMeans_DF_10,EqualMeans_DF_11,EqualMeans_DF_12,EqualMeans_DF_13)
    
    AR_DF <- rbind(AR_DF_1,AR_DF_2,AR_DF_3,AR_DF_4,AR_DF_5,AR_DF_6,AR_DF_7,AR_DF_8,AR_DF_9,AR_DF_10,AR_DF_11,AR_DF_12,AR_DF_13)
    
    ARI_DF <- rbind(ARI_DF_1,ARI_DF_2,ARI_DF_3,ARI_DF_4,ARI_DF_5,ARI_DF_6,ARI_DF_7,ARI_DF_8,ARI_DF_9,ARI_DF_10,ARI_DF_11,ARI_DF_12,ARI_DF_13)
    
    ARIS_DF <- rbind(ARIS_DF_1,ARIS_DF_2,ARIS_DF_3,ARIS_DF_4,ARIS_DF_5,ARIS_DF_6,ARIS_DF_7,ARIS_DF_8,ARIS_DF_9,ARIS_DF_10,ARIS_DF_11,ARIS_DF_12,ARIS_DF_13)
    
    
    EqualMeans_Results <- rbind(sum(EqualMeans_Results_1),sum(EqualMeans_Results_2),sum(EqualMeans_Results_3),sum(EqualMeans_Results_4),sum(EqualMeans_Results_5),
                                sum(EqualMeans_Results_6),sum(EqualMeans_Results_7),sum(EqualMeans_Results_8),sum(EqualMeans_Results_9),sum(EqualMeans_Results_10),
                                sum(EqualMeans_Results_11),sum(EqualMeans_Results_12),sum(EqualMeans_Results_13))
    
    AR_Results <- rbind(sum(AR_Results_1),sum(AR_Results_2),sum(AR_Results_3),sum(AR_Results_4),sum(AR_Results_5),sum(AR_Results_6),sum(AR_Results_7),
                        sum(AR_Results_8),sum(AR_Results_9),sum(AR_Results_10),sum(AR_Results_11),sum(AR_Results_12),sum(AR_Results_13))
    
    ARI_Results <- rbind(sum(ARI_Results_1),sum(ARI_Results_2),sum(ARI_Results_3),sum(ARI_Results_4),sum(ARI_Results_5),sum(ARI_Results_6),sum(ARI_Results_7),
                         sum(ARI_Results_8),sum(ARI_Results_9),sum(ARI_Results_10),sum(ARI_Results_11),sum(ARI_Results_12),sum(ARI_Results_13))
    
    ARIS_Results <- rbind(sum(ARIS_Results_1),sum(ARIS_Results_2),sum(ARIS_Results_3),sum(ARIS_Results_4),sum(ARIS_Results_5),sum(ARIS_Results_6),sum(ARIS_Results_7),
                         sum(ARIS_Results_8),sum(ARIS_Results_9),sum(ARIS_Results_10),sum(ARIS_Results_11),sum(ARIS_Results_12),sum(ARIS_Results_13))
    
    df_model = EqualMeans_DF - AR_DF
    ss_model = EqualMeans_Results - AR_Results
    ms_model = ss_model/df_model
    ms_ar = AR_Results/AR_DF
    F = ms_model/ms_ar
    AR_p_value = pf(F,df_model,AR_DF,lower.tail=FALSE)
    AR_p_tally = sum(AR_p_value[,1]<.05)
    results[i,"AR_F_Tally"] = AR_p_tally
    
    if (AR_p_tally >= 9){
      results[i,"AR_F_Conclusion"] = "Different"
    } else if (AR_p_tally <= 4){
      results[i,"AR_F_Conclusion"] = "Same"
    } else {
       results[i,"AR_F_Conclusion"] = "Inconclusive"
    }

    df_model = EqualMeans_DF - ARI_DF
    ss_model = EqualMeans_Results - ARI_Results
    ms_model = ss_model/df_model
    ms_ari = ARI_Results/ARI_DF
    F = ms_model/ms_ari
    ARI_p_value = pf(F,df_model,ARI_DF,lower.tail=FALSE)
    ARI_p_tally = sum(ARI_p_value[,1]<.05)
    results[i,"ARI_F_Tally"] = ARI_p_tally
    
    if (ARI_p_tally >= 9){
      results[i,"ARI_F_Conclusion"] = "Different"
    } else if (ARI_p_tally <= 4){
      results[i,"ARI_F_Conclusion"] = "Same"
    } else {
      results[i,"ARI_F_Conclusion"] = "Inconclusive"
    }
 
    df_model = EqualMeans_DF - ARIS_DF
    ss_model = EqualMeans_Results - ARIS_Results
    ms_model = ss_model/df_model
    ms_aris = ARIS_Results/ARIS_DF
    F = ms_model/ms_aris
    ARIS_p_value = pf(F,df_model,ARIS_DF,lower.tail=FALSE)
    ARIS_p_tally = sum(ARIS_p_value[,1]<.05)
    results[i,"ARIS_F_Tally"] = ARIS_p_tally
    
    if (ARIS_p_tally >= 9){
      results[i,"ARIS_F_Conclusion"] = "Different"
    } else if (ARIS_p_tally <= 4){
      results[i,"ARIS_F_Conclusion"] = "Same"
    } else {
       results[i,"ARIS_F_Conclusion"] = "Inconclusive"
    }

}

The Ljung-Box test with K=10 has a p-value of 4.786171e-12 .The Ljung-Box test with K=24 has a p-value of 1.665335e-15 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both tests for stationarity were inconclusive."

The Ljung-Box test with K=10 has a p-value of 0.08807377 .The Ljung-Box test with K=24 has a p-value of 0.3665865 .[1] "Ljung-Box test results: At a significance level of 0.05, we fail to reject the null hypothesis that this dataset is white noise."
[1] "One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise."
[1] "Both stationarity tests indicate this time series is NOT stationary."

The Ljung-Box test with K=10 has a p-value of 0.3801776 .The Ljung-Box test with K=24 has a p-value of 0.1126704 .[1] "Ljung-Box test results: At a significance level of 0.05, we fail to reject the null hypothesis that this dataset is white noise."
[1] "One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise."
[1] "Both tests for stationarity were inconclusive."

The Ljung-Box test with K=10 has a p-value of 0.0009489966 .The Ljung-Box test with K=24 has a p-value of 0.0002502709 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise."
[1] "Both tests for stationarity were inconclusive."

The Ljung-Box test with K=10 has a p-value of 0.0186233 .The Ljung-Box test with K=24 has a p-value of 0.005561031 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise."
[1] "Both tests for stationarity were inconclusive."

The Ljung-Box test with K=10 has a p-value of 6.426664e-08 .The Ljung-Box test with K=24 has a p-value of 6.568032e-10 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both stationarity tests indicate this time series is NOT stationary."

The Ljung-Box test with K=10 has a p-value of 2.934075e-10 .The Ljung-Box test with K=24 has a p-value of 3.874856e-11 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both tests for stationarity were inconclusive."

The Ljung-Box test with K=10 has a p-value of 0.6360152 .The Ljung-Box test with K=24 has a p-value of 0.844331 .[1] "Ljung-Box test results: At a significance level of 0.05, we fail to reject the null hypothesis that this dataset is white noise."
[1] "One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise."
[1] "Both stationarity tests indicate this time series is stationary."

The Ljung-Box test with K=10 has a p-value of 0.06656046 .The Ljung-Box test with K=24 has a p-value of 0.0002436308 .[1] "Ljung-Box test results: At a significance level of 0.05, the test is inconclusive."
[1] "One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise."
[1] "Both tests for stationarity were inconclusive."

The Ljung-Box test with K=10 has a p-value of 0.02684747 .The Ljung-Box test with K=24 has a p-value of 0.00508631 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise."
[1] "Both tests for stationarity were inconclusive."

results$winning_1 <- colnames(results[c("EqualMeans_1_ASE","AR_1_ASE","ARMA_1_ASE","ARI_1_ASE","ARIMA_1_ASE","ARI_S12_1_ASE","ARIMA_S12_1_ASE","RF_1_ASE","MLP_1_ASE")])[apply(results[c("EqualMeans_1_ASE","AR_1_ASE","ARMA_1_ASE","ARI_1_ASE","ARIMA_1_ASE","ARI_S12_1_ASE","ARIMA_S12_1_ASE","RF_1_ASE","MLP_1_ASE")],1,which.min)]

results$winning_2 <- colnames(results[c("EqualMeans_2_ASE","AR_2_ASE","ARMA_2_ASE","ARI_2_ASE","ARIMA_2_ASE","ARI_S12_2_ASE","ARIMA_S12_2_ASE","RF_2_ASE","MLP_2_ASE")])[apply(results[c("EqualMeans_2_ASE","AR_2_ASE","ARMA_2_ASE","ARI_2_ASE","ARIMA_2_ASE","ARI_S12_2_ASE","ARIMA_S12_2_ASE","RF_2_ASE","MLP_2_ASE")],1,which.min)]

results$winning_3 <- colnames(results[c("EqualMeans_3_ASE","AR_3_ASE","ARMA_3_ASE","ARI_3_ASE","ARIMA_3_ASE","ARI_S12_3_ASE","ARIMA_S12_3_ASE","RF_3_ASE","MLP_3_ASE")])[apply(results[c("EqualMeans_3_ASE","AR_3_ASE","ARMA_3_ASE","ARI_3_ASE","ARIMA_3_ASE","ARI_S12_3_ASE","ARIMA_S12_3_ASE","RF_3_ASE","MLP_3_ASE")],1,which.min)]

results$winning_4 <- colnames(results[c("EqualMeans_4_ASE","AR_4_ASE","ARMA_4_ASE","ARI_4_ASE","ARIMA_4_ASE","ARI_S12_4_ASE","ARIMA_S12_4_ASE","RF_4_ASE","MLP_4_ASE")])[apply(results[c("EqualMeans_4_ASE","AR_4_ASE","ARMA_4_ASE","ARI_4_ASE","ARIMA_4_ASE","ARI_S12_4_ASE","ARIMA_S12_4_ASE","RF_4_ASE","MLP_4_ASE")],1,which.min)]

results$winning_5 <- colnames(results[c("EqualMeans_5_ASE","AR_5_ASE","ARMA_5_ASE","ARI_5_ASE","ARIMA_5_ASE","ARI_S12_5_ASE","ARIMA_S12_5_ASE","RF_5_ASE","MLP_5_ASE")])[apply(results[c("EqualMeans_5_ASE","AR_5_ASE","ARMA_5_ASE","ARI_5_ASE","ARIMA_5_ASE","ARI_S12_5_ASE","ARIMA_S12_5_ASE","RF_5_ASE","MLP_5_ASE")],1,which.min)]

results$winning_6 <- colnames(results[c("EqualMeans_6_ASE","AR_6_ASE","ARMA_6_ASE","ARI_6_ASE","ARIMA_6_ASE","ARI_S12_6_ASE","ARIMA_S12_6_ASE","RF_6_ASE","MLP_6_ASE")])[apply(results[c("EqualMeans_6_ASE","AR_6_ASE","ARMA_6_ASE","ARI_6_ASE","ARIMA_6_ASE","ARI_S12_6_ASE","ARIMA_S12_6_ASE","RF_6_ASE","MLP_6_ASE")],1,which.min)]

results$winning_7 <- colnames(results[c("EqualMeans_7_ASE","AR_7_ASE","ARMA_7_ASE","ARI_7_ASE","ARIMA_7_ASE","ARI_S12_7_ASE","ARIMA_S12_7_ASE","RF_7_ASE","MLP_7_ASE")])[apply(results[c("EqualMeans_7_ASE","AR_7_ASE","ARMA_7_ASE","ARI_7_ASE","ARIMA_7_ASE","ARI_S12_7_ASE","ARIMA_S12_7_ASE","RF_7_ASE","MLP_7_ASE")],1,which.min)]

results$winning_8 <- colnames(results[c("EqualMeans_8_ASE","AR_8_ASE","ARMA_8_ASE","ARI_8_ASE","ARIMA_8_ASE","ARI_S12_8_ASE","ARIMA_S12_8_ASE","RF_8_ASE","MLP_8_ASE")])[apply(results[c("EqualMeans_8_ASE","AR_8_ASE","ARMA_8_ASE","ARI_8_ASE","ARIMA_8_ASE","ARI_S12_8_ASE","ARIMA_S12_8_ASE","RF_8_ASE","MLP_8_ASE")],1,which.min)]

results$winning_9 <- colnames(results[c("EqualMeans_9_ASE","AR_9_ASE","ARMA_9_ASE","ARI_9_ASE","ARIMA_9_ASE","ARI_S12_9_ASE","ARIMA_S12_9_ASE","RF_9_ASE","MLP_9_ASE")])[apply(results[c("EqualMeans_9_ASE","AR_9_ASE","ARMA_9_ASE","ARI_9_ASE","ARIMA_9_ASE","ARI_S12_9_ASE","ARIMA_S12_9_ASE","RF_9_ASE","MLP_9_ASE")],1,which.min)]

results$winning_10 <- colnames(results[c("EqualMeans_10_ASE","AR_10_ASE","ARMA_10_ASE","ARI_10_ASE","ARIMA_10_ASE","ARI_S12_10_ASE","ARIMA_S12_10_ASE","RF_10_ASE","MLP_10_ASE")])[apply(results[c("EqualMeans_10_ASE","AR_10_ASE","ARMA_10_ASE","ARI_10_ASE","ARIMA_10_ASE","ARI_S12_10_ASE","ARIMA_S12_10_ASE","RF_10_ASE","MLP_10_ASE")],1,which.min)]

results$winning_11 <- colnames(results[c("EqualMeans_11_ASE","AR_11_ASE","ARMA_11_ASE","ARI_11_ASE","ARIMA_11_ASE","ARI_S12_11_ASE","ARIMA_S12_11_ASE","RF_11_ASE","MLP_11_ASE")])[apply(results[c("EqualMeans_11_ASE","AR_11_ASE","ARMA_11_ASE","ARI_11_ASE","ARIMA_11_ASE","ARI_S12_11_ASE","ARIMA_S12_11_ASE","RF_11_ASE","MLP_11_ASE")],1,which.min)]

results$winning_12 <- colnames(results[c("EqualMeans_12_ASE","AR_12_ASE","ARMA_12_ASE","ARI_12_ASE","ARIMA_12_ASE","ARI_S12_12_ASE","ARIMA_S12_12_ASE","RF_12_ASE","MLP_12_ASE")])[apply(results[c("EqualMeans_12_ASE","AR_12_ASE","ARMA_12_ASE","ARI_12_ASE","ARIMA_12_ASE","ARI_S12_12_ASE","ARIMA_S12_12_ASE","RF_12_ASE","MLP_12_ASE")],1,which.min)]

formattable(results, align = c("l", rep("r", NCOL(table_a) - 1)))
Product_Type Product Customer ljung_10 ljung_24 ljung_results top_5_bic ADF KPSS stationarity_results EqualMeans_1_ASE EqualMeans_2_ASE EqualMeans_3_ASE EqualMeans_4_ASE EqualMeans_5_ASE EqualMeans_6_ASE EqualMeans_7_ASE EqualMeans_8_ASE EqualMeans_9_ASE EqualMeans_10_ASE EqualMeans_11_ASE EqualMeans_12_ASE EqualMeans_F1 EqualMeans_F2 EqualMeans_F3 EqualMeans_F4 EqualMeans_F5 EqualMeans_F6 EqualMeans_F7 EqualMeans_F8 EqualMeans_F9 EqualMeans_F10 EqualMeans_F11 EqualMeans_F12 AR_1_ASE AR_2_ASE AR_3_ASE AR_4_ASE AR_5_ASE AR_6_ASE AR_7_ASE AR_8_ASE AR_9_ASE AR_10_ASE AR_11_ASE AR_12_ASE AR_F1 AR_F2 AR_F3 AR_F4 AR_F5 AR_F6 AR_F7 AR_F8 AR_F9 AR_F10 AR_F11 AR_F12 ARMA_1_ASE ARMA_2_ASE ARMA_3_ASE ARMA_4_ASE ARMA_5_ASE ARMA_6_ASE ARMA_7_ASE ARMA_8_ASE ARMA_9_ASE ARMA_10_ASE ARMA_11_ASE ARMA_12_ASE ARMA_F1 ARMA_F2 ARMA_F3 ARMA_F4 ARMA_F5 ARMA_F6 ARMA_F7 ARMA_F8 ARMA_F9 ARMA_F10 ARMA_F11 ARMA_F12 ARI_1_ASE ARI_2_ASE ARI_3_ASE ARI_4_ASE ARI_5_ASE ARI_6_ASE ARI_7_ASE ARI_8_ASE ARI_9_ASE ARI_10_ASE ARI_11_ASE ARI_12_ASE ARI_F1 ARI_F2 ARI_F3 ARI_F4 ARI_F5 ARI_F6 ARI_F7 ARI_F8 ARI_F9 ARI_F10 ARI_F11 ARI_F12 ARIMA_1_ASE ARIMA_2_ASE ARIMA_3_ASE ARIMA_4_ASE ARIMA_5_ASE ARIMA_6_ASE ARIMA_7_ASE ARIMA_8_ASE ARIMA_9_ASE ARIMA_10_ASE ARIMA_11_ASE ARIMA_12_ASE ARIMA_F1 ARIMA_F2 ARIMA_F3 ARIMA_F4 ARIMA_F5 ARIMA_F6 ARIMA_F7 ARIMA_F8 ARIMA_F9 ARIMA_F10 ARIMA_F11 ARIMA_F12 ARI_S12_1_ASE ARI_S12_2_ASE ARI_S12_3_ASE ARI_S12_4_ASE ARI_S12_5_ASE ARI_S12_6_ASE ARI_S12_7_ASE ARI_S12_8_ASE ARI_S12_9_ASE ARI_S12_10_ASE ARI_S12_11_ASE ARI_S12_12_ASE ARI_S12_F1 ARI_S12_F2 ARI_S12_F3 ARI_S12_F4 ARI_S12_F5 ARI_S12_F6 ARI_S12_F7 ARI_S12_F8 ARI_S12_F9 ARI_S12_F10 ARI_S12_F11 ARI_S12_F12 ARIMA_S12_1_ASE ARIMA_S12_2_ASE ARIMA_S12_3_ASE ARIMA_S12_4_ASE ARIMA_S12_5_ASE ARIMA_S12_6_ASE ARIMA_S12_7_ASE ARIMA_S12_8_ASE ARIMA_S12_9_ASE ARIMA_S12_10_ASE ARIMA_S12_11_ASE ARIMA_S12_12_ASE ARIMA_S12_F1 ARIMA_S12_F2 ARIMA_S12_F3 ARIMA_S12_F4 ARIMA_S12_F5 ARIMA_S12_F6 ARIMA_S12_F7 ARIMA_S12_F8 ARIMA_S12_F9 ARIMA_S12_F10 ARIMA_S12_F11 ARIMA_S12_F12 RF_1_ASE RF_2_ASE RF_3_ASE RF_4_ASE RF_5_ASE RF_6_ASE RF_7_ASE RF_8_ASE RF_9_ASE RF_10_ASE RF_11_ASE RF_12_ASE RF_F1 RF_F2 RF_F3 RF_F4 RF_F5 RF_F6 RF_F7 RF_F8 RF_F9 RF_F10 RF_F11 RF_F12 MLP_1_ASE MLP_2_ASE MLP_3_ASE MLP_4_ASE MLP_5_ASE MLP_6_ASE MLP_7_ASE MLP_8_ASE MLP_9_ASE MLP_10_ASE MLP_11_ASE MLP_12_ASE MLP_F1 MLP_F2 MLP_F3 MLP_F4 MLP_F5 MLP_F6 MLP_F7 MLP_F8 MLP_F9 MLP_F10 MLP_F11 MLP_F12 ACTUAL_1 ACTUAL_2 ACTUAL_3 ACTUAL_4 ACTUAL_5 ACTUAL_6 ACTUAL_7 ACTUAL_8 ACTUAL_9 ACTUAL_10 ACTUAL_11 ACTUAL_12 AR_F_Tally AR_F_Conclusion ARI_F_Tally ARI_F_Conclusion ARIS_F_Tally ARIS_F_Conclusion winning_1 winning_2 winning_3 winning_4 winning_5 winning_6 winning_7 winning_8 winning_9 winning_10 winning_11 winning_12
700005895 JACK DANIELS BLK WHSKY 750M 700005895 4.786171e-12 1.665335e-15 not white noise NA 0.01000000 0.01000000 inconclusive 9.0689744 9.1510256 9.1886325 9.1215385 9.2110256 9.6625641 9.9165934 10.1410897 10.2612821 10.3625641 10.2468298 10.6138462 2.5666667 2.5666667 2.5666667 2.5666667 2.5666667 2.5666667 2.5666667 2.5666667 2.5666667 2.5666667 2.5666667 2.5666667 5.6054255 5.9078848 6.4067013 6.4869790 6.5917304 6.6944584 7.0349089 7.1368006 7.1971954 7.2508134 7.1868458 7.4055501 2.9385459 6.1082771 3.1081098 6.2741873 3.2881512 5.0736059 3.5813577 4.8597982 3.4703213 4.3656519 3.5756278 4.1122127 5.5392257 5.9681069 6.3616927 6.4042988 6.4227636 6.4027409 6.6372491 6.7007490 6.7862477 6.7964345 6.7325565 6.8699152 2.93854588 6.1082771 3.1081098 6.2741873 3.2881512 5.0736059 3.5813577 4.8597982 3.4703213 4.3656519 3.5756278 4.1122127 6.0065094 6.4548964 6.6022233 6.7586774 6.8199332 6.6568282 6.9602557 6.9366006 6.9896175 6.9462730 6.8550545 6.7939120 3.436980899 6.5566763 3.6522630 7.0612788 4.1406292 6.026328 4.6235795 6.0845704 4.687679 5.7308138 4.9907181 5.6522099 8.5418681 9.2801912 8.6697046 9.3972474 9.5739507 9.0672141 9.6068875 9.4353998 9.5065170 9.6750977 9.3342680 9.3124904 3.43698090 6.5566763 3.6522630 7.0612788 4.1406292 6.0263278 4.6235795 6.0845704 4.6876795 5.7308138 4.9907181 5.6522099 8.7661541 9.803003 9.924557 10.2763219 10.4523866 10.4310370 10.511161 10.458360 10.511135 10.486019 10.452995 9.991491 1.8534557 4.438188e+00 4.832533e+00 2.064003e+00 2.975539e+00 6.009348e+00 9.964272e-01 5.001365e+00 2.999478e+00 8.000199442 0.99992378 9.0000291 9.155954 9.981319 10.046597 10.254467 10.473186 10.450372 10.530208 10.474697 10.512969 10.469637 10.440687 9.977978 2.6914828 3.9313527 4.955730 1.9714508 2.98158891 5.9881269 0.992343155 4.99506218 2.9968157 7.997946449 0.9986757 8.9991460 6.0498044 6.9827080 7.0426996 7.0088504 6.9382068 6.9870023 7.0209966 7.1040564 7.1329618 7.3064732 7.1409205 6.9999049 4.678167 5.3755667 5.9625333 3.1371000 4.6781667 6.3589000 2.8396333 6.0982667 4.6948333 6.6237000 2.8396333 6.6237000 7.9375735 11.7480491 12.2976824 11.3134571 11.3812936 12.6606764 13.2381222 13.3745233 13.6682289 13.9975748 14.0103835 14.5946817 2.538217702 0.97899051 1.2940198 2.3134472 1.6646977 1.09209151 1.1568677 1.4891501 1.2349146 1.1074768 1.1229634 1.2105442 3 4 4 4 5 8 0 4 3.0 3 5 11 13 Different 13 Different 7 Inconclusive ARMA_1_ASE AR_2_ASE ARMA_3_ASE ARMA_4_ASE ARMA_5_ASE ARMA_6_ASE ARMA_7_ASE ARMA_8_ASE ARMA_9_ASE ARMA_10_ASE ARMA_11_ASE ARI_12_ASE
700005448 TORTILLA SILVER TEQ DSS 1.75L 700005448 8.807377e-02 3.665865e-01 white noise white noise 0.36870575 0.04762877 not stationary 0.5716556 0.5655017 0.5624248 0.5890915 0.6004761 0.6090060 0.6144394 0.6163350 0.6305729 0.6623222 0.6920285 0.7245188 1.7666667 1.7666667 1.7666667 1.7666667 1.7666667 1.7666667 1.7666667 1.7666667 1.7666667 1.7666667 1.7666667 1.7666667 0.6942115 0.6524714 0.6334266 0.6328648 0.6385497 0.6432841 0.6451130 0.6422000 0.6525317 0.6822315 0.7099566 0.7406985 1.3264075 1.8551896 1.7485388 2.1041247 1.5952620 1.8547966 1.8165794 1.8481962 1.7264328 1.8256658 1.7942109 1.7898796 0.7207688 0.6861532 0.6757951 0.6679848 0.6538848 0.6548755 0.6565445 0.6579988 0.6676573 0.6958380 0.7219311 0.7529246 1.32640746 1.8551896 1.7485388 2.1041247 1.5952620 1.8547966 1.8165794 1.8481962 1.7264328 1.8256658 1.7942109 1.7898796 0.7111108 0.6771035 0.6693311 0.6447135 0.6409545 0.6513507 0.6510615 0.6474969 0.6610099 0.6801487 0.7078773 0.7412894 1.483642804 1.6939099 1.8377815 2.0630840 1.8225134 1.744476 1.8927136 1.9130802 1.842049 1.8223885 1.8720112 1.8767798 0.6405925 0.6299260 0.6164646 0.6233314 0.6240543 0.6366802 0.6364920 0.6307053 0.6530211 0.6699885 0.6931830 0.7184782 1.75858628 1.2814051 2.3923115 1.6312175 2.3777548 1.1617182 2.5041757 1.5867593 2.0791025 1.7296408 1.9551375 2.0209115 1.1825183 1.156639 1.050869 0.9929159 0.9851617 0.9846825 0.993386 1.009069 1.014999 1.044005 1.057417 1.071727 1.3661099 1.853173e+00 2.515872e+00 1.392691e+00 1.793101e+00 2.130942e+00 1.244046e+00 3.060392e+00 9.889031e-01 2.110560127 1.08497928 3.0194668 2.032046 1.722801 1.651667 1.800139 2.099372 2.177397 2.211459 2.195750 2.284632 2.260631 2.206559 2.181600 2.6835456 0.4203508 3.786647 0.5895539 3.02059874 0.9706353 2.254651845 2.55529723 1.5109352 1.721572263 1.4321250 2.9702114 0.7128529 0.6605771 0.6448564 0.7148635 0.7476166 0.7601325 0.7766704 0.7946097 0.8120335 0.8453550 0.8714070 0.8945990 1.848867 1.8488667 1.8488667 1.0650667 1.8488667 1.8488667 1.0650667 2.7457000 1.0650667 1.8488667 1.0650667 2.7457000 0.5965944 0.6451668 0.6550854 0.6828447 0.6707437 0.6926139 0.7020487 0.7023441 0.7137983 0.7381717 0.7587158 0.7879413 1.656563945 2.32850043 1.5366885 1.6044749 1.8466523 1.54633712 1.5833060 1.6343155 1.5609408 1.5760818 1.5958171 1.5682539 3 2 2 3 2 2 2 2 0.0 0 1 3 0 Same 1 Same 0 Same EqualMeans_1_ASE EqualMeans_2_ASE EqualMeans_3_ASE EqualMeans_4_ASE EqualMeans_5_ASE EqualMeans_6_ASE EqualMeans_7_ASE EqualMeans_8_ASE EqualMeans_9_ASE EqualMeans_10_ASE EqualMeans_11_ASE ARIMA_12_ASE
701001904 FLOR DE CANA GOLD RUM 4YR 1L 701001904 3.801776e-01 1.126704e-01 white noise white noise 0.01799216 0.01000000 inconclusive 0.6995513 0.5290385 0.4687821 0.4425000 0.4523718 0.4589530 0.4816026 0.5017949 0.5197792 0.5367308 0.5501340 0.5606624 0.6500000 0.6500000 0.6500000 0.6500000 0.6500000 0.6500000 0.6500000 0.6500000 0.6500000 0.6500000 0.6500000 0.6500000 0.7495953 0.6475434 0.5938069 0.5412605 0.5349852 0.5315703 0.5433585 0.5522855 0.5613699 0.5713498 0.5802719 0.5876067 0.6189358 0.6527571 0.6497553 0.6500217 0.6499981 0.6500002 0.6500000 0.6500000 0.6500000 0.6500000 0.6500000 0.6500000 1.0442915 0.8301104 0.7067074 0.6343535 0.6128546 0.5994945 0.5999598 0.6006017 0.6010513 0.6102566 0.6137591 0.6163443 0.65000000 0.6500000 0.6500000 0.6500000 0.6500000 0.6500000 0.6500000 0.6500000 0.6500000 0.6500000 0.6500000 0.6500000 1.0349494 0.8290190 0.7312359 0.6620074 0.6296827 0.6136809 0.6087270 0.6020128 0.6082493 0.6280958 0.6405428 0.6497845 1.000000000 1.0000000 1.0000000 1.0000000 1.0000000 1.000000 1.0000000 1.0000000 1.000000 1.0000000 1.0000000 1.0000000 1.9471137 1.3335527 1.1635218 1.0611714 1.0070012 1.0167857 0.9846006 1.0169535 1.0343591 1.0306570 1.0266886 1.0104301 1.00000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 2.3016359 2.160235 2.157709 2.1207569 2.0960530 2.0694459 2.093314 2.033312 1.987007 1.957459 1.933255 1.913106 3.0000000 1.942890e-17 -3.608225e-17 -3.041192e-17 1.000000e+00 1.000000e+00 1.942890e-17 1.000000e+00 1.000000e+00 1.000000000 1.00000000 1.0000000 1.772864 2.322617 2.302087 2.249213 2.201378 2.157702 2.153409 2.092362 2.041340 2.006400 1.978361 1.954473 2.9999502 0.0000000 0.000000 0.0000000 1.00000000 1.0000000 0.000000000 1.00000000 1.0000000 1.000000000 1.0000000 1.0000000 1.3000939 1.1570493 1.1074100 1.0702476 1.0412809 1.0112418 0.9684744 0.9486574 0.9534083 0.9542528 0.9717126 0.9804113 1.750733 0.2715000 0.2715000 0.2715000 1.0675000 1.0675000 0.2715000 1.0675000 1.0675000 1.0675000 1.0675000 1.0675000 1.2378788 1.0097607 0.9069398 0.7724612 0.8176093 0.8655840 0.8303112 0.8940488 0.8803867 0.8891547 0.8730491 0.8718788 -0.003686558 0.07880159 0.1416579 0.9675949 0.2774209 0.05252596 0.8467427 0.2028610 0.5669621 0.4753789 0.7164548 0.6459699 0 2 1 0 2 1 2 0 0.0 0 1 1 0 Same 0 Same 0 Same EqualMeans_1_ASE EqualMeans_2_ASE EqualMeans_3_ASE EqualMeans_4_ASE EqualMeans_5_ASE EqualMeans_6_ASE EqualMeans_7_ASE EqualMeans_8_ASE EqualMeans_9_ASE EqualMeans_10_ASE EqualMeans_11_ASE EqualMeans_12_ASE
700005925 CASA NOBLE CRYSTAL TEQ 6PK 750M 700005925 9.489966e-04 2.502709e-04 not white noise white noise 0.56183917 0.10000000 inconclusive 3.1726068 3.2405556 2.7649145 2.5264530 2.3567094 2.2431197 2.1619841 2.0844658 2.0233191 1.9738889 1.9341453 1.8899145 1.3500000 1.3500000 1.3500000 1.3500000 1.3500000 1.3500000 1.3500000 1.3500000 1.3500000 1.3500000 1.3500000 1.3500000 4.5966191 4.3161665 3.4365422 3.1320838 2.7848548 2.5911752 2.4824384 2.3478787 2.2610588 2.1947776 2.1270249 2.0663430 0.7225347 0.8637380 1.1752617 1.0767431 1.1714654 1.2640872 1.2357247 1.2825245 1.3091095 1.3033956 1.3236393 1.3311831 4.6180807 4.3620508 3.4623764 3.1590933 2.8408239 2.6484569 2.5365775 2.3976202 2.3051311 2.2344015 2.1656202 2.1016788 0.72253469 0.8637380 1.1752617 1.0767431 1.1714654 1.2640872 1.2357247 1.2825245 1.3091095 1.3033956 1.3236393 1.3311831 5.7312374 5.0980361 4.1245420 3.6589359 3.2222853 3.1039759 2.8972426 2.6976785 2.6349594 2.4971475 2.4257860 2.3649153 0.003428975 0.2622852 0.5162665 0.2921546 0.2720958 0.400818 0.3365328 0.3104867 0.355351 0.3438979 0.3280937 0.3423912 5.7705099 5.0332742 4.0433952 3.6224390 3.1748973 3.0480544 2.8517410 2.6583122 2.6026693 2.4718678 2.3973343 2.3338023 -0.02714597 0.1918815 0.4429970 0.2198456 0.2550397 0.3166516 0.2686866 0.2734572 0.2882915 0.2780980 0.2784749 0.2819902 5.7135260 7.165921 7.422999 7.6199840 7.6454588 7.6091332 7.585894 7.541272 7.450487 7.374793 6.983284 6.654251 -2.4977111 6.729156e+00 -1.212209e+00 -1.273990e+00 2.624861e-01 -1.046592e+00 -3.388357e-01 -1.154433e-01 -6.015934e-01 -0.078887469 -0.22358983 0.7220991 6.311784 7.842069 8.196566 8.260550 8.124630 8.058478 7.944359 7.942456 7.808970 7.577955 7.185047 6.843732 -2.4977111 6.7291556 -1.212209 -1.2739896 0.26248613 -1.0465918 -0.338835725 -0.11544334 -0.6015934 -0.078887469 -0.2235898 0.7220991 5.5063671 6.4615421 6.8569428 6.9403913 6.8899397 6.6828534 6.4541674 6.3184049 6.0536568 5.8011695 5.5388071 5.3284908 1.259600 5.2485333 0.6839000 0.6839000 0.6839000 0.6839000 0.6839000 0.6839000 0.6839000 0.6839000 0.6839000 1.3386333 25.8647856 14.2830144 19.0885569 14.5709263 17.2296374 14.5200195 16.4182672 14.4743929 15.8403500 14.3436477 15.4783054 14.2539738 5.569774663 0.96383865 5.5458039 1.0589248 5.5445936 1.08410416 5.5445087 1.0884563 5.5445074 1.0892216 5.5445086 1.0893584 0 0 0 0 1 0 0 1 0.0 0 0 1 8 Inconclusive 8 Inconclusive 0 Same EqualMeans_1_ASE EqualMeans_2_ASE EqualMeans_3_ASE EqualMeans_4_ASE EqualMeans_5_ASE EqualMeans_6_ASE EqualMeans_7_ASE EqualMeans_8_ASE EqualMeans_9_ASE EqualMeans_10_ASE EqualMeans_11_ASE EqualMeans_12_ASE
701001770 PIRAS 51 CACHACA 80 1L 701001770 1.862330e-02 5.561031e-03 not white noise white noise 0.21808191 0.07405623 inconclusive 0.7631624 0.7772650 0.7768376 0.7029060 0.6354701 0.6046154 0.6243346 0.6400855 0.6620228 0.6680342 0.6624631 0.6627350 1.0500000 1.0500000 1.0500000 1.0500000 1.0500000 1.0500000 1.0500000 1.0500000 1.0500000 1.0500000 1.0500000 1.0500000 0.6498729 0.6709398 0.6600289 0.6062765 0.5525729 0.5312124 0.5595709 0.5828176 0.6105208 0.6213706 0.6200620 0.6239249 1.0432794 1.0490967 1.0498786 1.0499837 1.0499978 1.0499997 1.0500000 1.0500000 1.0500000 1.0500000 1.0500000 1.0500000 0.6446346 0.6657276 0.6525417 0.5925254 0.5308812 0.5020173 0.5298103 0.5568825 0.5879643 0.6020638 0.6045947 0.6120855 1.05000000 1.0500000 1.0500000 1.0500000 1.0500000 1.0500000 1.0500000 1.0500000 1.0500000 1.0500000 1.0500000 1.0500000 0.7803533 0.8929894 0.8497721 0.8027063 0.7675136 0.7567434 0.7859594 0.8179896 0.8364671 0.8647910 0.9235486 0.9779088 1.430652114 1.3249808 1.2159647 1.2516776 1.2945449 1.270597 1.2621083 1.2697373 1.272804 1.2690478 1.2688739 1.2699860 0.5001610 0.5698775 0.6161735 0.6000020 0.5748791 0.5755548 0.6115162 0.6488012 0.6920893 0.7273038 0.7643915 0.7972260 1.34886792 1.3488679 1.3488679 1.3488679 1.3488679 1.3488679 1.3488679 1.3488679 1.3488679 1.3488679 1.3488679 1.3488679 2.1299157 2.250523 2.379156 2.5211432 2.5465898 2.5717437 2.632695 2.668386 2.715570 2.727514 2.716594 2.652661 1.0000000 2.000000e+00 3.000000e+00 2.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 2.000000e+00 2.000000000 1.00000000 1.0000000 2.133433 2.262730 2.385876 2.528330 2.554339 2.586967 2.650574 2.684445 2.731844 2.739532 2.727685 2.665071 1.0000000 2.0000000 3.000000 2.0000000 1.00000000 1.0000000 1.000000000 1.00000000 2.0000000 2.000000000 1.0000000 1.0000000 1.5281369 1.5652216 1.7439732 1.8406330 1.7953375 1.7538955 1.7491473 1.7152193 1.7694161 1.8062429 1.7863637 1.7498799 1.655567 2.3852000 2.6609667 2.3852000 1.6555667 1.6555667 1.6555667 1.6555667 2.3852000 2.3852000 1.6555667 1.6555667 1.3086425 0.8759303 0.9172024 0.7938742 0.7221067 0.6717083 0.7000032 0.7194444 0.7387459 0.7402898 0.7304822 0.7326094 0.506872287 1.26454849 0.6144269 0.8672698 0.6422513 0.72214489 0.6497136 0.6719595 0.6517768 0.6577276 0.6523498 0.6540086 1 1 0 0 1 0 3 1 0.0 1 1 2 3 Same 2 Same 0 Same ARIMA_1_ASE ARIMA_2_ASE ARIMA_3_ASE ARMA_4_ASE ARMA_5_ASE ARMA_6_ASE ARMA_7_ASE ARMA_8_ASE ARMA_9_ASE ARMA_10_ASE ARMA_11_ASE ARMA_12_ASE
701001908 MCCORMICK VODKA 80 1.75L 701001908 6.426664e-08 6.568032e-10 not white noise NA 0.35666834 0.01740497 not stationary 2.2285256 2.4682692 2.0174145 1.8387821 1.7351923 1.6960470 1.6831044 1.6737179 1.6755342 1.6782692 1.6840035 1.6919872 1.5166667 1.5166667 1.5166667 1.5166667 1.5166667 1.5166667 1.5166667 1.5166667 1.5166667 1.5166667 1.5166667 1.5166667 2.4832483 2.7884601 2.5526392 2.4921262 2.4662996 2.4860781 2.4224876 2.3582667 2.3111059 2.2122487 2.1354672 2.0701868 1.3401307 1.1609156 2.2917969 1.4780675 1.2880298 1.9169957 1.5267468 1.3762987 1.7208581 1.5387184 1.4333333 1.6194098 2.6388001 2.9401760 2.8495561 2.5864904 2.3975025 2.3198086 2.2665143 2.2897757 2.3101477 2.2679359 2.1984358 2.1269990 1.34013071 1.1609156 2.2917969 1.4780675 1.2880298 1.9169957 1.5267468 1.3762987 1.7208581 1.5387184 1.4333333 1.6194098 2.8287590 3.0922478 2.9173888 3.0093555 3.0584183 3.1341009 3.0941062 2.9857088 2.9088922 2.7147794 2.5400621 2.4206506 1.419774355 1.2906208 2.4812131 1.6294789 1.4822995 2.185309 1.7312375 1.6057336 2.017685 1.7786510 1.6837401 1.9233905 2.8193328 3.1843995 3.1282574 3.0207945 2.9848679 3.0366704 2.9866854 2.8984773 2.8083638 2.6253766 2.4693641 2.3587800 1.01860624 1.0478045 2.2427166 1.4686003 1.2267672 1.8538817 1.6050905 1.3785051 1.6742643 1.6258436 1.4753673 1.6002531 2.7180753 2.731890 2.603679 2.3893369 2.2532880 2.2452744 2.215078 2.217877 2.233337 2.231591 2.235785 2.232764 0.6407034 5.500378e+00 1.791860e+00 7.559485e-01 9.272458e-01 2.295159e+00 8.820483e-01 2.140238e-02 1.105101e+00 0.953093899 1.02782941 3.0364945 2.718075 2.731890 2.603679 2.389337 2.253288 2.245274 2.215078 2.217877 2.233337 2.231591 2.235785 2.232764 0.6407034 5.5003778 1.791860 0.7559485 0.92724581 2.2951594 0.882048312 0.02140238 1.1051015 0.953093899 1.0278294 3.0364945 2.0267153 1.8918195 1.7548877 1.6352237 1.6274658 1.6535894 1.6483592 1.6804013 1.6895730 1.6768923 1.6980926 1.6920025 1.060400 4.0770667 1.0604000 1.0604000 1.0604000 1.8818667 1.0604000 0.4446000 1.0604000 1.0604000 1.0604000 2.8422667 2.0697694 10.0793992 7.5857859 6.0418036 6.8814292 6.0415395 5.4113769 7.4222835 6.7802824 6.2774426 6.6811277 6.2740434 1.535367414 6.00781067 0.4133082 1.3716830 4.4929023 0.94921962 1.5348301 6.2202014 1.4905833 1.3581906 4.2693955 1.4464008 2 4 3 0 2 0 0 2 0.0 1 2 2 2 Same 2 Same 0 Same RF_1_ASE RF_2_ASE RF_3_ASE RF_4_ASE RF_5_ASE RF_6_ASE RF_7_ASE EqualMeans_8_ASE EqualMeans_9_ASE RF_10_ASE EqualMeans_11_ASE EqualMeans_12_ASE
700005926 MCCORMICK VODKA 80 TRVL 750M 700005926 2.934075e-10 3.874856e-11 not white noise NA 0.07556121 0.10000000 inconclusive 0.6716239 0.5062393 0.4528205 0.4171368 0.3767521 0.3481197 0.3262027 0.3161752 0.3018234 0.2911111 0.2919037 0.2927778 1.1500000 1.1500000 1.1500000 1.1500000 1.1500000 1.1500000 1.1500000 1.1500000 1.1500000 1.1500000 1.1500000 1.1500000 0.6182281 0.4551938 0.4304193 0.4188211 0.3983483 0.3700911 0.3485136 0.3334866 0.3165183 0.3033057 0.3013792 0.2992889 1.3711375 1.1760882 1.2549802 1.2993734 1.2362031 1.1794933 1.2001215 1.1423049 1.1184965 1.1244998 1.1167234 1.1133609 0.5968163 0.4579625 0.4497181 0.4511265 0.4286348 0.4049576 0.3825204 0.3637018 0.3428458 0.3270631 0.3227980 0.3181758 1.37113745 1.1760882 1.2549802 1.2993734 1.2362031 1.1794933 1.2001215 1.1423049 1.1184965 1.1244998 1.1167234 1.1133609 0.6994756 0.5598007 0.5893693 0.6548900 0.6911132 0.6870577 0.6978623 0.7013999 0.6918955 0.6905217 0.6916737 0.6876350 1.000000000 1.0000000 1.0000000 1.0000000 1.0000000 1.000000 1.0000000 1.0000000 1.000000 1.0000000 1.0000000 1.0000000 0.7227470 0.5716485 0.6012171 0.6667377 0.7006763 0.6931936 0.7031823 0.7046800 0.6948582 0.6932306 0.6941748 0.6899631 1.00000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 2.0011501 1.388384 1.393567 1.2746320 1.1727551 1.0914126 1.030270 1.024978 1.018166 1.005870 1.003606 1.002454 3.0000000 1.000000e+00 2.000000e+00 2.000000e+00 1.000000e+00 -2.386980e-16 1.000000e+00 -2.664535e-16 1.000000e+00 1.000000000 1.00000000 1.0000000 2.242084 1.956935 2.049454 1.863884 1.727736 1.549117 1.558636 1.507911 1.542104 1.495994 1.398345 1.408520 3.0000000 1.0000000 2.000000 2.0000000 1.00000000 0.0000000 1.000000000 0.00000000 1.0000000 1.000000000 1.0000000 1.0000000 1.2265354 0.9759582 0.8768046 0.7840333 0.7018179 0.6620587 0.6297858 0.6420082 0.6422437 0.6392397 0.6457699 0.6497929 2.286700 0.9794333 1.8411667 1.8411667 0.9794333 0.1454333 0.9794333 0.1454333 0.9794333 0.9794333 0.9794333 0.9794333 0.6084604 0.4682055 0.4123026 0.4405396 0.4195244 0.3984964 0.3871777 0.3772918 0.3850468 0.3739793 0.3805600 0.3832535 1.007112861 1.14212264 1.0166948 1.4969534 0.5846710 1.42631843 0.8403497 1.2238527 0.9389953 1.9732302 1.4297120 1.7914312 1 1 1 2 1 1 2 2 1.0 1 0 1 3 Same 0 Same 0 Same ARMA_1_ASE AR_2_ASE MLP_3_ASE EqualMeans_4_ASE EqualMeans_5_ASE EqualMeans_6_ASE EqualMeans_7_ASE EqualMeans_8_ASE EqualMeans_9_ASE EqualMeans_10_ASE EqualMeans_11_ASE EqualMeans_12_ASE
701001850 RICH & RARE CANADIAN RSV 6PK 750M 701001850 6.360152e-01 8.443310e-01 white noise white noise 0.03437467 0.10000000 stationary 11.9384353 10.4039481 9.9608284 10.6224737 10.8606404 11.0467686 11.1601569 11.2330186 11.2435663 11.3251840 11.5126614 11.6416917 4.1616667 4.1616667 4.1616667 4.1616667 4.1616667 4.1616667 4.1616667 4.1616667 4.1616667 4.1616667 4.1616667 4.1616667 11.4489409 10.1784232 9.8099232 10.5092017 10.7700050 10.9712374 11.0954158 11.1763701 11.1932121 11.2798652 11.4714625 11.6039260 4.1798794 4.1596149 4.1618978 4.1616406 4.1616696 4.1616663 4.1616667 4.1616667 4.1616667 4.1616667 4.1616667 4.1616667 10.9581620 10.7792516 11.0698208 12.0680550 12.0926064 12.3485626 12.1985500 12.0879789 12.0085145 12.0304265 12.1421225 12.2456236 5.80614173 2.8852428 5.0417073 3.5549156 4.5799961 3.8732461 4.3605205 4.0245653 4.2561923 4.0964952 4.2065997 4.1306873 13.0951858 11.6481072 11.1661089 12.4410030 13.0870605 12.8400163 12.9485012 13.0177933 12.7570510 12.8400437 12.8687104 12.6773155 3.780987287 1.8499237 3.1462242 2.8342741 3.0518430 3.021921 2.6582298 2.9916366 2.944486 2.8983373 2.9180147 2.8677563 15.9706679 14.2314006 12.0051347 14.2947521 14.6930887 14.8401812 14.7715397 15.1490428 14.9630577 15.3793237 15.4024611 15.4003271 0.58909996 1.0023861 1.0023861 1.0023861 1.0023861 1.0023861 1.0023861 1.0023861 1.0023861 1.0023861 1.0023861 1.0023861 16.4562445 18.766613 20.152105 20.9217712 19.5220324 18.6401552 17.977276 17.364732 16.904462 16.728555 16.479735 16.137770 11.0127590 1.627930e-04 5.000002e+00 9.000000e+00 3.381346e-10 2.000000e+00 5.000000e+00 7.000000e+00 4.997449e-17 4.000000000 1.00000000 4.0000000 15.974995 19.457766 19.705139 19.398040 17.880262 17.076971 16.550790 16.126107 15.784831 15.735607 15.589212 15.317253 11.0000000 0.0000000 5.000000 9.0000000 0.00000000 2.0000000 5.000000000 7.00000000 0.0000000 4.000000000 1.0000000 4.0000000 12.1384838 11.7215436 12.5130330 13.9877554 14.0829582 14.1292931 14.6592910 14.5272090 14.3196426 14.1653784 14.4699477 14.3462932 9.747967 1.5193000 5.4709300 7.1142467 1.5193000 2.8831133 5.1852767 6.5627467 1.5193000 4.2841967 1.8674333 4.2841967 11.7961948 10.4502693 10.0032988 10.7951898 11.0197483 11.1689675 11.2496409 11.3088068 11.2875094 11.3961481 11.5744275 11.6957635 3.629845634 3.59280893 3.5929578 3.5929568 3.5929568 3.59295678 3.5929568 3.5929568 3.5929568 3.5929568 3.5929568 3.5929568 6 8 0 11 0 0 4 5 1.7 9 0 2 0 Same 0 Same 0 Same ARMA_1_ASE AR_2_ASE AR_3_ASE AR_4_ASE AR_5_ASE AR_6_ASE AR_7_ASE AR_8_ASE AR_9_ASE AR_10_ASE AR_11_ASE AR_12_ASE
700005900 1800 SILVER TEQ 750M 700005900 6.656046e-02 2.436308e-04 inconclusive white noise 0.01000000 0.01000000 inconclusive 1.1171368 1.1107265 1.1102991 1.1081624 1.1017521 1.1201282 1.0706166 1.0338034 1.0060256 0.9840598 0.9670202 0.9756838 0.6333333 0.6333333 0.6333333 0.6333333 0.6333333 0.6333333 0.6333333 0.6333333 0.6333333 0.6333333 0.6333333 0.6333333 1.2694401 1.2353152 1.2111815 1.2005473 1.1928079 1.1889463 1.1321560 1.0856273 1.0529158 1.0258907 1.0064240 1.0109016 0.1864625 0.7794505 0.5855561 0.6489555 0.6282252 0.6350036 0.6327872 0.6335119 0.6332749 0.6333524 0.6333271 0.6333354 1.3180946 1.2112054 1.1772851 1.1584018 1.1419437 1.1536212 1.0993249 1.0589231 1.0283543 1.0041556 0.9852891 0.9924302 -0.05591195 0.6333333 0.6333333 0.6333333 0.6333333 0.6333333 0.6333333 0.6333333 0.6333333 0.6333333 0.6333333 0.6333333 0.9557315 1.0151942 1.0146379 1.0069576 0.9392117 0.9051722 0.8653613 0.8297796 0.8010411 0.7715015 0.7554179 0.7541395 0.268686968 1.2008117 1.0003608 0.9785906 1.5935426 1.133580 0.7655984 1.2496301 1.076164 1.1593790 1.2569435 1.0189189 1.5081476 1.4503722 1.2940762 1.3000560 1.1782780 1.1161573 1.0581466 1.0076505 0.9827825 0.9540515 0.9299877 0.9175731 0.64265601 0.9245660 0.8978135 0.8021449 1.3182205 1.5003782 1.1435372 0.9864337 0.9272725 0.9557136 1.1530119 1.2810937 0.9574296 1.184131 1.377686 1.4540277 1.5115846 1.5065743 1.469295 1.438855 1.416015 1.397798 1.410954 1.402502 0.5151459 -2.653753e-01 1.367070e-01 1.929576e+00 3.627866e-02 2.981311e+00 9.627461e-03 9.950405e-01 1.002555e+00 -0.001316141 2.00067800 1.9996507 1.240651 1.421723 1.520543 1.556107 1.579133 1.557323 1.510084 1.475001 1.447865 1.426175 1.436418 1.425711 0.5151459 -0.2653753 0.136707 1.9295759 0.03627866 2.9813112 0.009627461 0.99504045 1.0025549 -0.001316141 2.0006780 1.9996507 1.0889227 1.1938315 1.2078672 1.1971481 1.1526314 1.1048728 1.0634745 1.0395780 1.0151023 0.9866821 0.9944546 0.9601414 0.925900 0.9259000 0.9259000 2.2016333 0.9259000 2.2636333 0.9259000 1.8691667 1.8691667 0.9259000 2.2016333 2.2016333 1.7626608 1.3982429 1.3505134 1.2944042 1.2719159 1.2784103 1.2171923 1.1711803 1.1363217 1.1076894 1.0844674 1.0909853 0.071294378 0.65838041 0.4123800 0.5241567 0.4754183 0.49742335 0.4873554 0.4919707 0.4898566 0.4908254 0.4903815 0.4905849 1 1 1 1 2 2 1 1 1.0 1 0 3 0 Same 8 Inconclusive 0 Same ARI_1_ASE ARI_2_ASE ARI_3_ASE ARI_4_ASE ARI_5_ASE ARI_6_ASE ARI_7_ASE ARI_8_ASE ARI_9_ASE ARI_10_ASE ARI_11_ASE ARI_12_ASE
701001907 FIREBALL CINN WHSKY NL 1.75L 701001907 2.684747e-02 5.086310e-03 not white noise white noise 0.04668965 0.01000000 inconclusive 3.4168803 3.3079060 2.9254274 2.7130342 2.5886752 2.5040598 2.4198107 2.3614316 2.3071937 2.2732906 2.2324981 2.2626068 1.6000000 1.6000000 1.6000000 1.6000000 1.6000000 1.6000000 1.6000000 1.6000000 1.6000000 1.6000000 1.6000000 1.6000000 3.2898172 3.2366595 2.8775217 2.6771531 2.5599846 2.4801535 2.3993198 2.3435020 2.2912563 2.2589469 2.2194583 2.2506538 1.0668640 1.6835982 1.5868914 1.6020555 1.5996777 1.6000505 1.5999921 1.6000012 1.5999998 1.6000000 1.6000000 1.6000000 3.7157148 3.4365654 3.1173311 2.9231418 2.8139887 2.7461842 2.6322659 2.5592011 2.4549392 2.3839704 2.3220255 2.3329799 1.60000000 1.6000000 1.6000000 1.6000000 1.6000000 1.6000000 1.6000000 1.6000000 1.6000000 1.6000000 1.6000000 1.6000000 4.3497572 4.2915776 4.1116214 4.0215718 3.8129812 3.8353961 3.6344605 3.4995624 3.3521435 3.1619863 3.1006578 3.0391359 1.546153990 2.1375851 2.8225759 1.9654009 2.8285898 2.225588 2.3534364 2.5281922 2.309131 2.4762238 2.3792225 2.3964842 5.8000703 5.1632613 4.7546005 4.5020618 4.4388272 4.0885904 3.9722412 3.9131948 3.7770898 3.7799643 3.7415046 3.8206163 1.54615399 2.1375851 2.8225759 1.9654009 2.8285898 2.2255880 2.3534364 2.5281922 2.3091314 2.4762238 2.3792225 2.3964842 3.7581676 4.541867 4.310137 4.2013851 4.0199866 3.8782900 3.797198 3.763896 3.745683 3.701350 3.610695 3.476131 2.9189758 4.426907e+00 3.427754e-01 -3.060416e-01 3.175670e+00 7.106078e-02 9.099376e-01 2.376254e-02 1.970290e+00 3.014569540 0.01796634 4.9892791 3.409515 4.526630 5.475029 6.034526 5.773231 5.414569 5.320162 5.250294 5.147824 4.962384 4.771355 4.783543 2.5322567 5.0000000 0.000000 0.0000000 3.00000000 0.0000000 1.000000000 0.00000000 2.0000000 3.000000000 0.0000000 5.0000000 3.1179416 3.4747325 3.3036057 3.3439456 3.1473544 3.0340253 2.9631910 2.8960751 2.8821119 2.8307555 2.7583684 2.6500130 2.994033 3.8158667 0.5009333 0.5009333 2.9940333 0.5009333 1.0086333 0.5009333 2.1698000 2.9940333 0.5009333 3.8158667 3.2041042 3.7331123 4.1548037 3.8221708 3.8675977 4.0147802 4.0880622 4.1436985 4.2124801 4.2932663 4.5847800 4.5473579 1.726126015 2.51047722 2.8769059 2.0924927 2.6680562 2.88333626 3.1890527 3.6491556 3.5744128 3.2024774 4.2617630 3.8282143 1 2 1 1 3 0 2 2 1.0 3 1 5 1 Same 0 Same 0 Same RF_1_ASE AR_2_ASE AR_3_ASE AR_4_ASE AR_5_ASE AR_6_ASE AR_7_ASE AR_8_ASE AR_9_ASE AR_10_ASE AR_11_ASE AR_12_ASE

Forecast Aggregation by Product


'data.frame':   2436 obs. of  5 variables:
 $ date        : Factor w/ 84 levels "1/1/2013","1/1/2014",..: 1 29 36 43 50 57 64 71 78 8 ...
 $ Product_Type: Factor w/ 57 levels "ABSINTHE","AMARETTO",..: 49 49 49 49 49 49 49 49 49 49 ...
 $ Product     : Factor w/ 4017 levels "1800 ANEJO TEQ 6PK 750M",..: 2325 2325 2325 2325 2325 2325 2325 2325 2325 2325 ...
 $ Customer_ID : int  700005925 700005925 700005925 700005925 700005925 700005925 700005925 700005925 700005925 700005925 ...
 $ n           : int  84 84 84 84 84 84 84 84 84 84 ...
'data.frame':   2436 obs. of  7 variables:
 $ date        : chr  "1/1/2013" "2/1/2013" "3/1/2013" "4/1/2013" ...
 $ Product_Type: Factor w/ 57 levels "ABSINTHE","AMARETTO",..: 49 49 49 49 49 49 49 49 49 49 ...
 $ Product     : Factor w/ 4017 levels "1800 ANEJO TEQ 6PK 750M",..: 2325 2325 2325 2325 2325 2325 2325 2325 2325 2325 ...
 $ Customer_ID : int  700005925 700005925 700005925 700005925 700005925 700005925 700005925 700005925 700005925 700005925 ...
 $ n           : int  84 84 84 84 84 84 84 84 84 84 ...
 $ STD_Cases   : num  53.8 58 67 68 72 66 72 72 44 49.8 ...
 $ Dollar_Sales: num  3135 3379 3903 3961 4194 ...
'data.frame':   336 obs. of  7 variables:
 $ date        : chr  "1/1/2013" "2/1/2013" "3/1/2013" "4/1/2013" ...
 $ Product_Type: Factor w/ 57 levels "ABSINTHE","AMARETTO",..: 49 49 49 49 49 49 49 49 49 49 ...
 $ Product     : Factor w/ 4017 levels "1800 ANEJO TEQ 6PK 750M",..: 2325 2325 2325 2325 2325 2325 2325 2325 2325 2325 ...
 $ Customer_ID : int  700005895 700005895 700005895 700005895 700005895 700005895 700005895 700005895 700005895 700005895 ...
 $ n           : int  39 39 39 39 39 39 39 39 39 39 ...
 $ STD_Cases   : num  2 0 0 1 1 0 0 0 0 0 ...
 $ Dollar_Sales: num  117 0 0 58 58 0 0 0 0 0 ...
# this loop is for forcasting all customers individually for one product

z = nrow(combinations)
results <- data.frame(Product_Type=integer(),
                      Product=character(),
                      Customer=integer(),
                      ljung_10=double(),
                      ljung_24=double(),
                      ljung_results=character(),
                      top_5_bic=character(),
                      ADF=double(),
                      KPSS=double(),
                      stationarity_results=character(),
                      EqualMeans_1_ASE=double(),
                      EqualMeans_2_ASE=double(),
                      EqualMeans_3_ASE=double(),
                      EqualMeans_4_ASE=double(),
                      EqualMeans_5_ASE=double(),
                      EqualMeans_6_ASE=double(),
                      EqualMeans_7_ASE=double(),
                      EqualMeans_8_ASE=double(),
                      EqualMeans_9_ASE=double(),
                      EqualMeans_10_ASE=double(),
                      EqualMeans_11_ASE=double(),
                      EqualMeans_12_ASE=double(),
                      EqualMeans_F1=double(),
                      EqualMeans_F2=double(),
                      EqualMeans_F3=double(),
                      EqualMeans_F4=double(),
                      EqualMeans_F5=double(),
                      EqualMeans_F6=double(),
                      EqualMeans_F7=double(),
                      EqualMeans_F8=double(),
                      EqualMeans_F9=double(),
                      EqualMeans_F10=double(),
                      EqualMeans_F11=double(),
                      EqualMeans_F12=double(),
                      AR_1_ASE=double(),
                      AR_2_ASE=double(),
                      AR_3_ASE=double(),
                      AR_4_ASE=double(),
                      AR_5_ASE=double(),
                      AR_6_ASE=double(),
                      AR_7_ASE=double(),
                      AR_8_ASE=double(),
                      AR_9_ASE=double(),
                      AR_10_ASE=double(),
                      AR_11_ASE=double(),
                      AR_12_ASE=double(),
                      AR_F1=double(),
                      AR_F2=double(),
                      AR_F3=double(),
                      AR_F4=double(),
                      AR_F5=double(),
                      AR_F6=double(),
                      AR_F7=double(),
                      AR_F8=double(),
                      AR_F9=double(),
                      AR_F10=double(),
                      AR_F11=double(),
                      AR_F12=double(),
                      ARMA_1_ASE=double(),
                      ARMA_2_ASE=double(),
                      ARMA_3_ASE=double(),
                      ARMA_4_ASE=double(),
                      ARMA_5_ASE=double(),
                      ARMA_6_ASE=double(),
                      ARMA_7_ASE=double(),
                      ARMA_8_ASE=double(),
                      ARMA_9_ASE=double(),
                      ARMA_10_ASE=double(),
                      ARMA_11_ASE=double(),
                      ARMA_12_ASE=double(),
                      ARMA_F1=double(),
                      ARMA_F2=double(),
                      ARMA_F3=double(),
                      ARMA_F4=double(),
                      ARMA_F5=double(),
                      ARMA_F6=double(),
                      ARMA_F7=double(),
                      ARMA_F8=double(),
                      ARMA_F9=double(),
                      ARMA_F10=double(),
                      ARMA_F11=double(),
                      ARMA_F12=double(),
                      ARI_1_ASE=double(),
                      ARI_2_ASE=double(),
                      ARI_3_ASE=double(),
                      ARI_4_ASE=double(),
                      ARI_5_ASE=double(),
                      ARI_6_ASE=double(),
                      ARI_7_ASE=double(),
                      ARI_8_ASE=double(),
                      ARI_9_ASE=double(),
                      ARI_10_ASE=double(),
                      ARI_11_ASE=double(),
                      ARI_12_ASE=double(),
                      ARI_F1=double(),
                      ARI_F2=double(),
                      ARI_F3=double(),
                      ARI_F4=double(),
                      ARI_F5=double(),
                      ARI_F6=double(),
                      ARI_F7=double(),
                      ARI_F8=double(),
                      ARI_F9=double(),
                      ARI_F10=double(),
                      ARI_F11=double(),
                      ARI_F12=double(),
                      ARIMA_1_ASE=double(),
                      ARIMA_2_ASE=double(),
                      ARIMA_3_ASE=double(),
                      ARIMA_4_ASE=double(),
                      ARIMA_5_ASE=double(),
                      ARIMA_6_ASE=double(),
                      ARIMA_7_ASE=double(),
                      ARIMA_8_ASE=double(),
                      ARIMA_9_ASE=double(),
                      ARIMA_10_ASE=double(),
                      ARIMA_11_ASE=double(),
                      ARIMA_12_ASE=double(),
                      ARIMA_F1=double(),
                      ARIMA_F2=double(),
                      ARIMA_F3=double(),
                      ARIMA_F4=double(),
                      ARIMA_F5=double(),
                      ARIMA_F6=double(),
                      ARIMA_F7=double(),
                      ARIMA_F8=double(),
                      ARIMA_F9=double(),
                      ARIMA_F10=double(),
                      ARIMA_F11=double(),
                      ARIMA_F12=double(),
                      ARI_S12_1_ASE=double(),
                      ARI_S12_2_ASE=double(),
                      ARI_S12_3_ASE=double(),
                      ARI_S12_4_ASE=double(),
                      ARI_S12_5_ASE=double(),
                      ARI_S12_6_ASE=double(),
                      ARI_S12_7_ASE=double(),
                      ARI_S12_8_ASE=double(),
                      ARI_S12_9_ASE=double(),
                      ARI_S12_10_ASE=double(),
                      ARI_S12_11_ASE=double(),
                      ARI_S12_12_ASE=double(),
                      ARI_S12_F1=double(),
                      ARI_S12_F2=double(),
                      ARI_S12_F3=double(),
                      ARI_S12_F4=double(),
                      ARI_S12_F5=double(),
                      ARI_S12_F6=double(),
                      ARI_S12_F7=double(),
                      ARI_S12_F8=double(),
                      ARI_S12_F9=double(),
                      ARI_S12_F10=double(),
                      ARI_S12_F11=double(),
                      ARI_S12_F12=double(),
                      ARIMA_S12_1_ASE=double(),
                      ARIMA_S12_2_ASE=double(),
                      ARIMA_S12_3_ASE=double(),
                      ARIMA_S12_4_ASE=double(),
                      ARIMA_S12_5_ASE=double(),
                      ARIMA_S12_6_ASE=double(),
                      ARIMA_S12_7_ASE=double(),
                      ARIMA_S12_8_ASE=double(),
                      ARIMA_S12_9_ASE=double(),
                      ARIMA_S12_10_ASE=double(),
                      ARIMA_S12_11_ASE=double(),
                      ARIMA_S12_12_ASE=double(),
                      ARIMA_S12_F1=double(),
                      ARIMA_S12_F2=double(),
                      ARIMA_S12_F3=double(),
                      ARIMA_S12_F4=double(),
                      ARIMA_S12_F5=double(),
                      ARIMA_S12_F6=double(),
                      ARIMA_S12_F7=double(),
                      ARIMA_S12_F8=double(),
                      ARIMA_S12_F9=double(),
                      ARIMA_S12_F10=double(),
                      ARIMA_S12_F11=double(),
                      ARIMA_S12_F12=double(),
                      RF_1_ASE=double(),
                      RF_2_ASE=double(),
                      RF_3_ASE=double(),
                      RF_4_ASE=double(),
                      RF_5_ASE=double(),
                      RF_6_ASE=double(),
                      RF_7_ASE=double(),
                      RF_8_ASE=double(),
                      RF_9_ASE=double(),
                      RF_10_ASE=double(),
                      RF_11_ASE=double(),
                      RF_12_ASE=double(),
                      RF_F1=double(),
                      RF_F2=double(),
                      RF_F3=double(),
                      RF_F4=double(),
                      RF_F5=double(),
                      RF_F6=double(),
                      RF_F7=double(),
                      RF_F8=double(),
                      RF_F9=double(),
                      RF_F10=double(),
                      RF_F11=double(),
                      RF_F12=double(),
                      MLP_1_ASE=double(),
                      MLP_2_ASE=double(),
                      MLP_3_ASE=double(),
                      MLP_4_ASE=double(),
                      MLP_5_ASE=double(),
                      MLP_6_ASE=double(),
                      MLP_7_ASE=double(),
                      MLP_8_ASE=double(),
                      MLP_9_ASE=double(),
                      MLP_10_ASE=double(),
                      MLP_11_ASE=double(),
                      MLP_12_ASE=double(),
                      MLP_F1=double(),
                      MLP_F2=double(),
                      MLP_F3=double(),
                      MLP_F4=double(),
                      MLP_F5=double(),
                      MLP_F6=double(),
                      MLP_F7=double(),
                      MLP_F8=double(),
                      MLP_F9=double(),
                      MLP_F10=double(),
                      MLP_F11=double(),
                      MLP_F12=double(),
                      ACTUAL_1=double(),
                      ACTUAL_2=double(),
                      ACTUAL_3=double(),
                      ACTUAL_4=double(),
                      ACTUAL_5=double(),
                      ACTUAL_6=double(),
                      ACTUAL_7=double(),
                      ACTUAL_8=double(),
                      ACTUAL_9=double(),
                      ACTUAL_10=double(),
                      ACTUAL_11=double(),
                      ACTUAL_12=double(),
                      AR_F_Tally=double(),
                      AR_F_Conclusion=double(),
                      ARI_F_Tally=double(),
                      ARI_F_Conclusion=double(),
                      ARIS_F_Tally=double(),
                      ARIS_F_Conclusion=double(),
                      stringsAsFactors = FALSE)

# loop through sample combinations
for(i in 1:z) {
  sample_combinations1 = combinations[i,]
  temp1 = inner_join(temp,sample_combinations1)
  product = sample_combinations1$Product
  customer = sample_combinations1$Customer_ID
  product_type = sample_combinations1$Customer_ID
  
  results[i,"Product_Type"] = product_type
  results[i,"Product"] = as.character(sample_combinations1$Product)
  results[i,"Customer"] = customer
  
  par(mfrow=c(1,1))
  plot.ts(temp1$STD_Cases, 
          main=c(paste("Standard Case Sales of ", product), 
                 paste("for Customer",customer)),
          xlab="Months",
          ylab="Standard Cases")
  
  par(mfrow = c(2,2))
  invisible(acf(temp1$STD_Cases, main="ACF"))
  invisible(parzen.wge(temp1$STD_Cases))

  invisible(acf(temp1$STD_Cases[0:length(temp1$date)/2], main="ACF for 1st Half of Series"))
  invisible(acf(temp1$STD_Cases[(1+length(temp1$date)/2):length(temp1$date)], main="ACF for 2nd Half of Series"))
  
  sink("file")
  ljung_10 = ljung.wge(temp1$STD_Cases,K=10)
  sink()
  cat("The Ljung-Box test with K=10 has a p-value of",ljung_10$pval,".")
  results[i,"ljung_10"] = ljung_10$pval
  
  sink("file")
  ljung_24 = ljung.wge(temp1$STD_Cases,K=24)
  sink()
  cat("The Ljung-Box test with K=24 has a p-value of",ljung_24$pval,".")
  results[i,"ljung_24"] = ljung_24$pval
  
  if (ljung_10$pval < .05 & ljung_24$pval < .05){
    print("Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise.")
    results[i,"ljung_results"] = "not white noise"
  } else if (ljung_10$pval > .05 & ljung_24$pval < .05){
    print("Ljung-Box test results: At a significance level of 0.05, the test is inconclusive.")
    results[i,"ljung_results"] = "inconclusive"
  } else if (ljung_10$pval < .05 & ljung_24$pval > .05){
    print("Ljung-Box test results: At a significance level of 0.05, the test is inconclusive.")
    results[i,"ljung_results"] = "inconclusive"
  } else {
    print("Ljung-Box test results: At a significance level of 0.05, we fail to reject the null hypothesis that this dataset is white noise.")
    results[i,"ljung_results"] = "white noise"
  }
  
  sink("file")
  aic = invisible(aic5.wge(temp1$STD_Cases,type="bic"))
  sink()
  
  for (row in 1:nrow(aic)) {
    if(aic[row,1] == 0 & aic[row,2] == 0){
      print("One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise.")
      results[i,"top_5_bic"] = "white noise"
    }
  }
  
  # Tests for stationarity
  
  # Augmented Dickey-Fuller
  adf=tseries::adf.test(temp1$STD_Cases)
  results[i,"ADF"] = adf$p.value
  
  # Kwiatkowski-Phillips-Schmidt-Shin
  kpss=tseries::kpss.test(temp1$STD_Cases)
  results[i,"KPSS"] = kpss$p.value
  
  if (adf$p.value < .05 &  kpss$p.value > .05){
    print("Both stationarity tests indicate this time series is stationary.")
    results[i,"stationarity_results"] = "stationary"
  } else if (adf$p.value >= .05 & kpss$p.value <= .05){
    print("Both stationarity tests indicate this time series is NOT stationary.")
    results[i,"stationarity_results"] = "not stationary"
  } else {
    print("Both tests for stationarity were inconclusive.")
    results[i,"stationarity_results"] = "inconclusive"
  }
  
  j=12
  
  #Equal Means Model
  
  trainingSize = 60
  ASEHolder1 = numeric()
  ASEHolder2 = numeric()
  ASEHolder3 = numeric()
  ASEHolder4 = numeric()
  ASEHolder5 = numeric()
  ASEHolder6 = numeric()
  ASEHolder7 = numeric()
  ASEHolder8 = numeric()
  ASEHolder9 = numeric()
  ASEHolder10 = numeric()
  ASEHolder11 = numeric()
  ASEHolder12 = numeric()

  for( k in 1:(84-(trainingSize + j) + 1))
  {
    sink("file")
    model0_mean = mean(temp1$STD_Cases[k:(k+(trainingSize-1))])
    ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - model0_mean)^2)
    ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - model0_mean)^2)
    ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - model0_mean)^2)
    ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - model0_mean)^2)
    ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - model0_mean)^2)
    ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - model0_mean)^2)
    ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - model0_mean)^2)
    ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - model0_mean)^2)
    ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - model0_mean)^2)
    ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - model0_mean)^2)
    ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - model0_mean)^2)
    ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - model0_mean)^2)
    sink()
    
    assign(paste("EqualMeans_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - model0_mean)^2)
    assign(paste("EqualMeans_DF_",k,sep=""),trainingSize-1)
  }
  
  WindowedASE1 = mean(ASEHolder1)
  WindowedASE2 = mean(ASEHolder2)
  WindowedASE3 = mean(ASEHolder3)
  WindowedASE4 = mean(ASEHolder4)
  WindowedASE5 = mean(ASEHolder5)
  WindowedASE6 = mean(ASEHolder6)
  WindowedASE7 = mean(ASEHolder7)
  WindowedASE8 = mean(ASEHolder8)
  WindowedASE9 = mean(ASEHolder9)
  WindowedASE10 = mean(ASEHolder10)
  WindowedASE11 = mean(ASEHolder11)
  WindowedASE12 = mean(ASEHolder12)
  results[i,paste0("EqualMeans_1_ASE")] = WindowedASE1
  results[i,paste0("EqualMeans_2_ASE")] = WindowedASE2
  results[i,paste0("EqualMeans_3_ASE")] = WindowedASE3
  results[i,paste0("EqualMeans_4_ASE")] = WindowedASE4
  results[i,paste0("EqualMeans_5_ASE")] = WindowedASE5
  results[i,paste0("EqualMeans_6_ASE")] = WindowedASE6
  results[i,paste0("EqualMeans_7_ASE")] = WindowedASE7
  results[i,paste0("EqualMeans_8_ASE")] = WindowedASE8
  results[i,paste0("EqualMeans_9_ASE")] = WindowedASE9
  results[i,paste0("EqualMeans_10_ASE")] = WindowedASE10
  results[i,paste0("EqualMeans_11_ASE")] = WindowedASE11
  results[i,paste0("EqualMeans_12_ASE")] = WindowedASE12
  results[i,paste0("EqualMeans_F1")] = model0_mean  
  results[i,paste0("EqualMeans_F2")] = model0_mean  
  results[i,paste0("EqualMeans_F3")] = model0_mean  
  results[i,paste0("EqualMeans_F4")] = model0_mean  
  results[i,paste0("EqualMeans_F5")] = model0_mean  
  results[i,paste0("EqualMeans_F6")] = model0_mean  
  results[i,paste0("EqualMeans_F7")] = model0_mean  
  results[i,paste0("EqualMeans_F8")] = model0_mean  
  results[i,paste0("EqualMeans_F9")] = model0_mean  
  results[i,paste0("EqualMeans_F10")] = model0_mean  
  results[i,paste0("EqualMeans_F11")] = model0_mean  
  results[i,paste0("EqualMeans_F12")] = model0_mean  

  #AR Model
  
  trainingSize = 60
  ASEHolder1 = numeric()
  ASEHolder2 = numeric()
  ASEHolder3 = numeric()
  ASEHolder4 = numeric()
  ASEHolder5 = numeric()
  ASEHolder6 = numeric()
  ASEHolder7 = numeric()
  ASEHolder8 = numeric()
  ASEHolder9 = numeric()
  ASEHolder10 = numeric()
  ASEHolder11 = numeric()
  ASEHolder12 = numeric()
  
  for( k in 1:(84-(trainingSize + j) + 1))
  {
    sink("file")
    model1 = invisible(aic.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],q=0,type="aic"))
    if (model1$p == 0){
      newphi = 1
    } else {
      newphi = model1$p
    } 
    model1_est = invisible(est.ar.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],p=newphi))
    forecasts = fore.aruma.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],phi = model1_est$phi, theta = 0, s = 0, d = 0,n.ahead = j,plot=FALSE)

    ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - forecasts$f[1:1])^2)
    ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - forecasts$f[1:2])^2)
    ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - forecasts$f[1:3])^2)
    ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - forecasts$f[1:4])^2)
    ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - forecasts$f[1:5])^2)
    ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - forecasts$f[1:6])^2)
    ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - forecasts$f[1:7])^2)
    ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - forecasts$f[1:8])^2)
    ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - forecasts$f[1:9])^2)
    ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - forecasts$f[1:10])^2)
    ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - forecasts$f[1:11])^2)
    ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - forecasts$f[1:12])^2)
    sink()
    
    assign(paste("AR_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - forecasts$f)^2)
    assign(paste("AR_DF_",k,sep=""),trainingSize-(newphi+1))

  }
  
  WindowedASE1 = mean(ASEHolder1)
  WindowedASE2 = mean(ASEHolder2)
  WindowedASE3 = mean(ASEHolder3)
  WindowedASE4 = mean(ASEHolder4)
  WindowedASE5 = mean(ASEHolder5)
  WindowedASE6 = mean(ASEHolder6)
  WindowedASE7 = mean(ASEHolder7)
  WindowedASE8 = mean(ASEHolder8)
  WindowedASE9 = mean(ASEHolder9)
  WindowedASE10 = mean(ASEHolder10)
  WindowedASE11 = mean(ASEHolder11)
  WindowedASE12 = mean(ASEHolder12)
  results[i,paste0("AR_1_ASE")] = WindowedASE1
  results[i,paste0("AR_2_ASE")] = WindowedASE2
  results[i,paste0("AR_3_ASE")] = WindowedASE3
  results[i,paste0("AR_4_ASE")] = WindowedASE4
  results[i,paste0("AR_5_ASE")] = WindowedASE5
  results[i,paste0("AR_6_ASE")] = WindowedASE6
  results[i,paste0("AR_7_ASE")] = WindowedASE7
  results[i,paste0("AR_8_ASE")] = WindowedASE8
  results[i,paste0("AR_9_ASE")] = WindowedASE9
  results[i,paste0("AR_10_ASE")] = WindowedASE10
  results[i,paste0("AR_11_ASE")] = WindowedASE11
  results[i,paste0("AR_12_ASE")] = WindowedASE12
  results[i,paste0("AR_F1")] = forecasts$f[1]  
  results[i,paste0("AR_F2")] = forecasts$f[2]   
  results[i,paste0("AR_F3")] = forecasts$f[3]   
  results[i,paste0("AR_F4")] = forecasts$f[4]   
  results[i,paste0("AR_F5")] = forecasts$f[5]   
  results[i,paste0("AR_F6")] = forecasts$f[6]   
  results[i,paste0("AR_F7")] = forecasts$f[7]   
  results[i,paste0("AR_F8")] = forecasts$f[8]   
  results[i,paste0("AR_F9")] = forecasts$f[9]   
  results[i,paste0("AR_F10")] = forecasts$f[10]   
  results[i,paste0("AR_F11")] = forecasts$f[11]   
  results[i,paste0("AR_F12")] = forecasts$f[12]  

  
  #ARMA Model
  
  trainingSize = 60
  ASEHolder1 = numeric()
  ASEHolder2 = numeric()
  ASEHolder3 = numeric()
  ASEHolder4 = numeric()
  ASEHolder5 = numeric()
  ASEHolder6 = numeric()
  ASEHolder7 = numeric()
  ASEHolder8 = numeric()
  ASEHolder9 = numeric()
  ASEHolder10 = numeric()
  ASEHolder11 = numeric()
  ASEHolder12 = numeric()
  
  for( k in 1:(84-(trainingSize + j) + 1))
  {
    sink("file")
    model1 = invisible(aic.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],type="aic"))
    model1_est = invisible(est.arma.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],p=model1$p,q=model1$q))
    forecasts = fore.aruma.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],phi = model1_est$phi, theta = model1_est$theta, s = 0, d = 0,n.ahead = j,plot=FALSE)

    ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - forecasts$f[1:1])^2)
    ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - forecasts$f[1:2])^2)
    ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - forecasts$f[1:3])^2)
    ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - forecasts$f[1:4])^2)
    ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - forecasts$f[1:5])^2)
    ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - forecasts$f[1:6])^2)
    ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - forecasts$f[1:7])^2)
    ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - forecasts$f[1:8])^2)
    ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - forecasts$f[1:9])^2)
    ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - forecasts$f[1:10])^2)
    ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - forecasts$f[1:11])^2)
    ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - forecasts$f[1:12])^2)
    sink()
    
    assign(paste("ARMA_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - forecasts$f)^2)

  }
  
  WindowedASE1 = mean(ASEHolder1)
  WindowedASE2 = mean(ASEHolder2)
  WindowedASE3 = mean(ASEHolder3)
  WindowedASE4 = mean(ASEHolder4)
  WindowedASE5 = mean(ASEHolder5)
  WindowedASE6 = mean(ASEHolder6)
  WindowedASE7 = mean(ASEHolder7)
  WindowedASE8 = mean(ASEHolder8)
  WindowedASE9 = mean(ASEHolder9)
  WindowedASE10 = mean(ASEHolder10)
  WindowedASE11 = mean(ASEHolder11)
  WindowedASE12 = mean(ASEHolder12)
  results[i,paste0("ARMA_1_ASE")] = WindowedASE1
  results[i,paste0("ARMA_2_ASE")] = WindowedASE2
  results[i,paste0("ARMA_3_ASE")] = WindowedASE3
  results[i,paste0("ARMA_4_ASE")] = WindowedASE4
  results[i,paste0("ARMA_5_ASE")] = WindowedASE5
  results[i,paste0("ARMA_6_ASE")] = WindowedASE6
  results[i,paste0("ARMA_7_ASE")] = WindowedASE7
  results[i,paste0("ARMA_8_ASE")] = WindowedASE8
  results[i,paste0("ARMA_9_ASE")] = WindowedASE9
  results[i,paste0("ARMA_10_ASE")] = WindowedASE10
  results[i,paste0("ARMA_11_ASE")] = WindowedASE11
  results[i,paste0("ARMA_12_ASE")] = WindowedASE12
  results[i,paste0("ARMA_F1")] = forecasts$f[1]  
  results[i,paste0("ARMA_F2")] = forecasts$f[2]   
  results[i,paste0("ARMA_F3")] = forecasts$f[3]   
  results[i,paste0("ARMA_F4")] = forecasts$f[4]   
  results[i,paste0("ARMA_F5")] = forecasts$f[5]   
  results[i,paste0("ARMA_F6")] = forecasts$f[6]   
  results[i,paste0("ARMA_F7")] = forecasts$f[7]   
  results[i,paste0("ARMA_F8")] = forecasts$f[8]   
  results[i,paste0("ARMA_F9")] = forecasts$f[9]   
  results[i,paste0("ARMA_F10")] = forecasts$f[10]   
  results[i,paste0("ARMA_F11")] = forecasts$f[11]   
  results[i,paste0("ARMA_F12")] = forecasts$f[12]  

  
  
  #ARIMA Model with q=0 and d=1
  nulldev()
  temp2 = artrans.wge(temp1$STD_Cases,1)
  dev.off()
  
  trainingSize = 60
  ASEHolder1 = numeric()
  ASEHolder2 = numeric()
  ASEHolder3 = numeric()
  ASEHolder4 = numeric()
  ASEHolder5 = numeric()
  ASEHolder6 = numeric()
  ASEHolder7 = numeric()
  ASEHolder8 = numeric()
  ASEHolder9 = numeric()
  ASEHolder10 = numeric()
  ASEHolder11 = numeric()
  ASEHolder12 = numeric()
    
  for( k in 1:(84-(trainingSize + j) + 1))
  {
    sink("file")
    model1 = invisible(aic.wge(temp2[k:(k+(trainingSize-1-1))],q=0,type="aic"))
    model1_est = invisible(est.ar.wge(temp2[k:(k+(trainingSize-1-1))],p=model1$p))
    forecasts = fore.aruma.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],phi = model1_est$phi, theta = 0, s = 0, d = 1,n.ahead = j,plot=FALSE)
    ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - forecasts$f[1:1])^2)
    ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - forecasts$f[1:2])^2)
    ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - forecasts$f[1:3])^2)
    ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - forecasts$f[1:4])^2)
    ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - forecasts$f[1:5])^2)
    ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - forecasts$f[1:6])^2)
    ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - forecasts$f[1:7])^2)
    ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - forecasts$f[1:8])^2)
    ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - forecasts$f[1:9])^2)
    ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - forecasts$f[1:10])^2)
    ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - forecasts$f[1:11])^2)
    ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - forecasts$f[1:12])^2)
    sink()
    
    assign(paste("ARI_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - forecasts$f)^2)
    assign(paste("ARI_DF_",k,sep=""),trainingSize-(model1$p+1))

  }
  
  WindowedASE1 = mean(ASEHolder1)
  WindowedASE2 = mean(ASEHolder2)
  WindowedASE3 = mean(ASEHolder3)
  WindowedASE4 = mean(ASEHolder4)
  WindowedASE5 = mean(ASEHolder5)
  WindowedASE6 = mean(ASEHolder6)
  WindowedASE7 = mean(ASEHolder7)
  WindowedASE8 = mean(ASEHolder8)
  WindowedASE9 = mean(ASEHolder9)
  WindowedASE10 = mean(ASEHolder10)
  WindowedASE11 = mean(ASEHolder11)
  WindowedASE12 = mean(ASEHolder12)
  results[i,paste0("ARI_1_ASE")] = WindowedASE1
  results[i,paste0("ARI_2_ASE")] = WindowedASE2
  results[i,paste0("ARI_3_ASE")] = WindowedASE3
  results[i,paste0("ARI_4_ASE")] = WindowedASE4
  results[i,paste0("ARI_5_ASE")] = WindowedASE5
  results[i,paste0("ARI_6_ASE")] = WindowedASE6
  results[i,paste0("ARI_7_ASE")] = WindowedASE7
  results[i,paste0("ARI_8_ASE")] = WindowedASE8
  results[i,paste0("ARI_9_ASE")] = WindowedASE9
  results[i,paste0("ARI_10_ASE")] = WindowedASE10
  results[i,paste0("ARI_11_ASE")] = WindowedASE11
  results[i,paste0("ARI_12_ASE")] = WindowedASE12
  results[i,paste0("ARI_F1")] = forecasts$f[1]  
  results[i,paste0("ARI_F2")] = forecasts$f[2]   
  results[i,paste0("ARI_F3")] = forecasts$f[3]   
  results[i,paste0("ARI_F4")] = forecasts$f[4]   
  results[i,paste0("ARI_F5")] = forecasts$f[5]   
  results[i,paste0("ARI_F6")] = forecasts$f[6]   
  results[i,paste0("ARI_F7")] = forecasts$f[7]   
  results[i,paste0("ARI_F8")] = forecasts$f[8]   
  results[i,paste0("ARI_F9")] = forecasts$f[9]   
  results[i,paste0("ARI_F10")] = forecasts$f[10]   
  results[i,paste0("ARI_F11")] = forecasts$f[11]   
  results[i,paste0("ARI_F12")] = forecasts$f[12]

  
  #ARIMA Model with d=1
  nulldev()
  temp2 = artrans.wge(temp1$STD_Cases,1)
  dev.off()
  
  trainingSize = 60
  ASEHolder1 = numeric()
  ASEHolder2 = numeric()
  ASEHolder3 = numeric()
  ASEHolder4 = numeric()
  ASEHolder5 = numeric()
  ASEHolder6 = numeric()
  ASEHolder7 = numeric()
  ASEHolder8 = numeric()
  ASEHolder9 = numeric()
  ASEHolder10 = numeric()
  ASEHolder11 = numeric()
  ASEHolder12 = numeric()
    
  for( k in 1:(84-(trainingSize + j) + 1))
  {
    sink("file")
    model1 = invisible(aic.wge(temp2[k:(k+(trainingSize-1-1))],type="aic"))
    model1_est = invisible(est.arma.wge(temp2[k:(k+(trainingSize-1-1))],p=model1$p,q=model1$q))
    forecasts = fore.aruma.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],phi = model1_est$phi, theta = model1_est$theta, s = 0, d = 1,n.ahead = j,plot=FALSE)
    ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - forecasts$f[1:1])^2)
    ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - forecasts$f[1:2])^2)
    ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - forecasts$f[1:3])^2)
    ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - forecasts$f[1:4])^2)
    ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - forecasts$f[1:5])^2)
    ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - forecasts$f[1:6])^2)
    ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - forecasts$f[1:7])^2)
    ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - forecasts$f[1:8])^2)
    ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - forecasts$f[1:9])^2)
    ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - forecasts$f[1:10])^2)
    ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - forecasts$f[1:11])^2)
    ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - forecasts$f[1:12])^2)
    sink()
    
    assign(paste("ARIMA_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - forecasts$f)^2)

  }
  
  WindowedASE1 = mean(ASEHolder1)
  WindowedASE2 = mean(ASEHolder2)
  WindowedASE3 = mean(ASEHolder3)
  WindowedASE4 = mean(ASEHolder4)
  WindowedASE5 = mean(ASEHolder5)
  WindowedASE6 = mean(ASEHolder6)
  WindowedASE7 = mean(ASEHolder7)
  WindowedASE8 = mean(ASEHolder8)
  WindowedASE9 = mean(ASEHolder9)
  WindowedASE10 = mean(ASEHolder10)
  WindowedASE11 = mean(ASEHolder11)
  WindowedASE12 = mean(ASEHolder12)
  results[i,paste0("ARIMA_1_ASE")] = WindowedASE1
  results[i,paste0("ARIMA_2_ASE")] = WindowedASE2
  results[i,paste0("ARIMA_3_ASE")] = WindowedASE3
  results[i,paste0("ARIMA_4_ASE")] = WindowedASE4
  results[i,paste0("ARIMA_5_ASE")] = WindowedASE5
  results[i,paste0("ARIMA_6_ASE")] = WindowedASE6
  results[i,paste0("ARIMA_7_ASE")] = WindowedASE7
  results[i,paste0("ARIMA_8_ASE")] = WindowedASE8
  results[i,paste0("ARIMA_9_ASE")] = WindowedASE9
  results[i,paste0("ARIMA_10_ASE")] = WindowedASE10
  results[i,paste0("ARIMA_11_ASE")] = WindowedASE11
  results[i,paste0("ARIMA_12_ASE")] = WindowedASE12
  results[i,paste0("ARIMA_F1")] = forecasts$f[1]  
  results[i,paste0("ARIMA_F2")] = forecasts$f[2]   
  results[i,paste0("ARIMA_F3")] = forecasts$f[3]   
  results[i,paste0("ARIMA_F4")] = forecasts$f[4]   
  results[i,paste0("ARIMA_F5")] = forecasts$f[5]   
  results[i,paste0("ARIMA_F6")] = forecasts$f[6]   
  results[i,paste0("ARIMA_F7")] = forecasts$f[7]   
  results[i,paste0("ARIMA_F8")] = forecasts$f[8]   
  results[i,paste0("ARIMA_F9")] = forecasts$f[9]   
  results[i,paste0("ARIMA_F10")] = forecasts$f[10]   
  results[i,paste0("ARIMA_F11")] = forecasts$f[11]   
  results[i,paste0("ARIMA_F12")] = forecasts$f[12]

  
 
#ARIMA Model with q=0 and S=12
  nulldev()
  temp2 = artrans.wge(temp1$STD_Cases,phi.tr=c(rep(0,11),1))
  dev.off()
  
  trainingSize = 60
  ASEHolder1 = numeric()
  ASEHolder2 = numeric()
  ASEHolder3 = numeric()
  ASEHolder4 = numeric()
  ASEHolder5 = numeric()
  ASEHolder6 = numeric()
  ASEHolder7 = numeric()
  ASEHolder8 = numeric()
  ASEHolder9 = numeric()
  ASEHolder10 = numeric()
  ASEHolder11 = numeric()
  ASEHolder12 = numeric()
  
  for( k in 1:(84-(trainingSize + j) + 1))
  {
    sink("file")
    model1 = invisible(aic.wge(temp2[k:(k+(trainingSize-1-12))],q=0, type="aic"))
    if (model1$p == 0){
      newphi = 1
    } else {
      newphi = model1$p
    } 
    model1_est = invisible(est.ar.wge(temp2[k:(k+(trainingSize-1-12))],p=newphi))
    forecasts = fore.aruma.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],phi = model1_est$phi, theta = 0, s = 12, d = 0,n.ahead = j,plot=FALSE)
    ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - forecasts$f[1:1])^2)
    ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - forecasts$f[1:2])^2)
    ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - forecasts$f[1:3])^2)
    ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - forecasts$f[1:4])^2)
    ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - forecasts$f[1:5])^2)
    ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - forecasts$f[1:6])^2)
    ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - forecasts$f[1:7])^2)
    ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - forecasts$f[1:8])^2)
    ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - forecasts$f[1:9])^2)
    ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - forecasts$f[1:10])^2)
    ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - forecasts$f[1:11])^2)
    ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - forecasts$f[1:12])^2)
    sink()
    
    assign(paste("ARIS_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - forecasts$f)^2)
    assign(paste("ARIS_DF_",k,sep=""),trainingSize-(newphi+1))

  }
  
  WindowedASE1 = mean(ASEHolder1)
  WindowedASE2 = mean(ASEHolder2)
  WindowedASE3 = mean(ASEHolder3)
  WindowedASE4 = mean(ASEHolder4)
  WindowedASE5 = mean(ASEHolder5)
  WindowedASE6 = mean(ASEHolder6)
  WindowedASE7 = mean(ASEHolder7)
  WindowedASE8 = mean(ASEHolder8)
  WindowedASE9 = mean(ASEHolder9)
  WindowedASE10 = mean(ASEHolder10)
  WindowedASE11 = mean(ASEHolder11)
  WindowedASE12 = mean(ASEHolder12)
  results[i,paste0("ARI_S12_1_ASE")] = WindowedASE1
  results[i,paste0("ARI_S12_2_ASE")] = WindowedASE2
  results[i,paste0("ARI_S12_3_ASE")] = WindowedASE3
  results[i,paste0("ARI_S12_4_ASE")] = WindowedASE4
  results[i,paste0("ARI_S12_5_ASE")] = WindowedASE5
  results[i,paste0("ARI_S12_6_ASE")] = WindowedASE6
  results[i,paste0("ARI_S12_7_ASE")] = WindowedASE7
  results[i,paste0("ARI_S12_8_ASE")] = WindowedASE8
  results[i,paste0("ARI_S12_9_ASE")] = WindowedASE9
  results[i,paste0("ARI_S12_10_ASE")] = WindowedASE10
  results[i,paste0("ARI_S12_11_ASE")] = WindowedASE11
  results[i,paste0("ARI_S12_12_ASE")] = WindowedASE12
  results[i,paste0("ARI_S12_F1")] = forecasts$f[1]  
  results[i,paste0("ARI_S12_F2")] = forecasts$f[2]   
  results[i,paste0("ARI_S12_F3")] = forecasts$f[3]   
  results[i,paste0("ARI_S12_F4")] = forecasts$f[4]   
  results[i,paste0("ARI_S12_F5")] = forecasts$f[5]   
  results[i,paste0("ARI_S12_F6")] = forecasts$f[6]   
  results[i,paste0("ARI_S12_F7")] = forecasts$f[7]   
  results[i,paste0("ARI_S12_F8")] = forecasts$f[8]   
  results[i,paste0("ARI_S12_F9")] = forecasts$f[9]   
  results[i,paste0("ARI_S12_F10")] = forecasts$f[10]   
  results[i,paste0("ARI_S12_F11")] = forecasts$f[11]   
  results[i,paste0("ARI_S12_F12")] = forecasts$f[12]   

  
  
  #ARIMA Model with S=12
  nulldev()
  temp2 = artrans.wge(temp1$STD_Cases,phi.tr=c(rep(0,11),1))
  dev.off()
  
  trainingSize = 60
  ASEHolder1 = numeric()
  ASEHolder2 = numeric()
  ASEHolder3 = numeric()
  ASEHolder4 = numeric()
  ASEHolder5 = numeric()
  ASEHolder6 = numeric()
  ASEHolder7 = numeric()
  ASEHolder8 = numeric()
  ASEHolder9 = numeric()
  ASEHolder10 = numeric()
  ASEHolder11 = numeric()
  ASEHolder12 = numeric()
  
  for( k in 1:(84-(trainingSize + j) + 1))
  {
    sink("file")
    model1 = invisible(aic.wge(temp2[k:(k+(trainingSize-1-12))],type="aic"))
    model1_est = invisible(est.arma.wge(temp2[k:(k+(trainingSize-1-12))],p=model1$p,q=model1$q))
    forecasts = fore.aruma.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],phi = model1_est$phi, theta = model1_est$theta, s = 12, d = 0,n.ahead = j,plot=FALSE)
    ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - forecasts$f[1:1])^2)
    ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - forecasts$f[1:2])^2)
    ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - forecasts$f[1:3])^2)
    ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - forecasts$f[1:4])^2)
    ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - forecasts$f[1:5])^2)
    ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - forecasts$f[1:6])^2)
    ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - forecasts$f[1:7])^2)
    ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - forecasts$f[1:8])^2)
    ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - forecasts$f[1:9])^2)
    ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - forecasts$f[1:10])^2)
    ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - forecasts$f[1:11])^2)
    ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - forecasts$f[1:12])^2)
    sink()
    
    assign(paste("ARIMAS_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - forecasts$f)^2)

  }
  
  WindowedASE1 = mean(ASEHolder1)
  WindowedASE2 = mean(ASEHolder2)
  WindowedASE3 = mean(ASEHolder3)
  WindowedASE4 = mean(ASEHolder4)
  WindowedASE5 = mean(ASEHolder5)
  WindowedASE6 = mean(ASEHolder6)
  WindowedASE7 = mean(ASEHolder7)
  WindowedASE8 = mean(ASEHolder8)
  WindowedASE9 = mean(ASEHolder9)
  WindowedASE10 = mean(ASEHolder10)
  WindowedASE11 = mean(ASEHolder11)
  WindowedASE12 = mean(ASEHolder12)
  results[i,paste0("ARIMA_S12_1_ASE")] = WindowedASE1
  results[i,paste0("ARIMA_S12_2_ASE")] = WindowedASE2
  results[i,paste0("ARIMA_S12_3_ASE")] = WindowedASE3
  results[i,paste0("ARIMA_S12_4_ASE")] = WindowedASE4
  results[i,paste0("ARIMA_S12_5_ASE")] = WindowedASE5
  results[i,paste0("ARIMA_S12_6_ASE")] = WindowedASE6
  results[i,paste0("ARIMA_S12_7_ASE")] = WindowedASE7
  results[i,paste0("ARIMA_S12_8_ASE")] = WindowedASE8
  results[i,paste0("ARIMA_S12_9_ASE")] = WindowedASE9
  results[i,paste0("ARIMA_S12_10_ASE")] = WindowedASE10
  results[i,paste0("ARIMA_S12_11_ASE")] = WindowedASE11
  results[i,paste0("ARIMA_S12_12_ASE")] = WindowedASE12
  results[i,paste0("ARIMA_S12_F1")] = forecasts$f[1]  
  results[i,paste0("ARIMA_S12_F2")] = forecasts$f[2]   
  results[i,paste0("ARIMA_S12_F3")] = forecasts$f[3]   
  results[i,paste0("ARIMA_S12_F4")] = forecasts$f[4]   
  results[i,paste0("ARIMA_S12_F5")] = forecasts$f[5]   
  results[i,paste0("ARIMA_S12_F6")] = forecasts$f[6]   
  results[i,paste0("ARIMA_S12_F7")] = forecasts$f[7]   
  results[i,paste0("ARIMA_S12_F8")] = forecasts$f[8]   
  results[i,paste0("ARIMA_S12_F9")] = forecasts$f[9]   
  results[i,paste0("ARIMA_S12_F10")] = forecasts$f[10]   
  results[i,paste0("ARIMA_S12_F11")] = forecasts$f[11]   
  results[i,paste0("ARIMA_S12_F12")] = forecasts$f[12]   

  
  
  #Random Forest
  trainingSize = 60
  ASEHolder1 = numeric()
  ASEHolder2 = numeric()
  ASEHolder3 = numeric()
  ASEHolder4 = numeric()
  ASEHolder5 = numeric()
  ASEHolder6 = numeric()
  ASEHolder7 = numeric()
  ASEHolder8 = numeric()
  ASEHolder9 = numeric()
  ASEHolder10 = numeric()
  ASEHolder11 = numeric()
  ASEHolder12 = numeric()
  
  for( k in 1:(84-(trainingSize + j) + 1))
  {
    sink("file")
   
    forecasts <- rf_ts(j, temp1[k:(k+(trainingSize-1)),], FALSE)
    
    ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - forecasts$forecast[1:1])^2)
    ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - forecasts$forecast[1:2])^2)
    ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - forecasts$forecast[1:3])^2)
    ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - forecasts$forecast[1:4])^2)
    ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - forecasts$forecast[1:5])^2)
    ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - forecasts$forecast[1:6])^2)
    ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - forecasts$forecast[1:7])^2)
    ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - forecasts$forecast[1:8])^2)
    ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - forecasts$forecast[1:9])^2)
    ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - forecasts$forecast[1:10])^2)
    ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - forecasts$forecast[1:11])^2)
    ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - forecasts$forecast[1:12])^2)
    sink()
    
    assign(paste("RF_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - forecasts$forecast)^2)

  }
  
  WindowedASE1 = mean(ASEHolder1)
  WindowedASE2 = mean(ASEHolder2)
  WindowedASE3 = mean(ASEHolder3)
  WindowedASE4 = mean(ASEHolder4)
  WindowedASE5 = mean(ASEHolder5)
  WindowedASE6 = mean(ASEHolder6)
  WindowedASE7 = mean(ASEHolder7)
  WindowedASE8 = mean(ASEHolder8)
  WindowedASE9 = mean(ASEHolder9)
  WindowedASE10 = mean(ASEHolder10)
  WindowedASE11 = mean(ASEHolder11)
  WindowedASE12 = mean(ASEHolder12)
  results[i,paste0("RF_1_ASE")] = WindowedASE1
  results[i,paste0("RF_2_ASE")] = WindowedASE2
  results[i,paste0("RF_3_ASE")] = WindowedASE3
  results[i,paste0("RF_4_ASE")] = WindowedASE4
  results[i,paste0("RF_5_ASE")] = WindowedASE5
  results[i,paste0("RF_6_ASE")] = WindowedASE6
  results[i,paste0("RF_7_ASE")] = WindowedASE7
  results[i,paste0("RF_8_ASE")] = WindowedASE8
  results[i,paste0("RF_9_ASE")] = WindowedASE9
  results[i,paste0("RF_10_ASE")] = WindowedASE10
  results[i,paste0("RF_11_ASE")] = WindowedASE11
  results[i,paste0("RF_12_ASE")] = WindowedASE12
  results[i,paste0("RF_F1")] = forecasts$forecast[1]  
  results[i,paste0("RF_F2")] = forecasts$forecast[2]   
  results[i,paste0("RF_F3")] = forecasts$forecast[3]   
  results[i,paste0("RF_F4")] = forecasts$forecast[4]   
  results[i,paste0("RF_F5")] = forecasts$forecast[5]   
  results[i,paste0("RF_F6")] = forecasts$forecast[6]   
  results[i,paste0("RF_F7")] = forecasts$forecast[7]   
  results[i,paste0("RF_F8")] = forecasts$forecast[8]   
  results[i,paste0("RF_F9")] = forecasts$forecast[9]   
  results[i,paste0("RF_F10")] = forecasts$forecast[10]   
  results[i,paste0("RF_F11")] = forecasts$forecast[11]   
  results[i,paste0("RF_F12")] = forecasts$forecast[12]   

  
  
  # MLP
  trainingSize = 60
  ASEHolder1 = numeric()
  ASEHolder2 = numeric()
  ASEHolder3 = numeric()
  ASEHolder4 = numeric()
  ASEHolder5 = numeric()
  ASEHolder6 = numeric()
  ASEHolder7 = numeric()
  ASEHolder8 = numeric()
  ASEHolder9 = numeric()
  ASEHolder10 = numeric()
  ASEHolder11 = numeric()
  ASEHolder12 = numeric()
  
  for( k in 1:(84-(trainingSize + j) + 1))
  {
    sink("file")

    forecasts <- nnc(temp1$STD_Cases[k:(k+(trainingSize-1))], j, 10, c(5, 10, 15, 5), FALSE)
    
    ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - forecasts$forecast[1:1])^2)
    ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - forecasts$forecast[1:2])^2)
    ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - forecasts$forecast[1:3])^2)
    ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - forecasts$forecast[1:4])^2)
    ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - forecasts$forecast[1:5])^2)
    ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - forecasts$forecast[1:6])^2)
    ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - forecasts$forecast[1:7])^2)
    ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - forecasts$forecast[1:8])^2)
    ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - forecasts$forecast[1:9])^2)
    ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - forecasts$forecast[1:10])^2)
    ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - forecasts$forecast[1:11])^2)
    ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - forecasts$forecast[1:12])^2)
    sink()
    
    assign(paste("MLP_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - forecasts$forecast)^2)

  }
  
  WindowedASE1 = mean(ASEHolder1)
  WindowedASE2 = mean(ASEHolder2)
  WindowedASE3 = mean(ASEHolder3)
  WindowedASE4 = mean(ASEHolder4)
  WindowedASE5 = mean(ASEHolder5)
  WindowedASE6 = mean(ASEHolder6)
  WindowedASE7 = mean(ASEHolder7)
  WindowedASE8 = mean(ASEHolder8)
  WindowedASE9 = mean(ASEHolder9)
  WindowedASE10 = mean(ASEHolder10)
  WindowedASE11 = mean(ASEHolder11)
  WindowedASE12 = mean(ASEHolder12)
  results[i,paste0("MLP_1_ASE")] = WindowedASE1
  results[i,paste0("MLP_2_ASE")] = WindowedASE2
  results[i,paste0("MLP_3_ASE")] = WindowedASE3
  results[i,paste0("MLP_4_ASE")] = WindowedASE4
  results[i,paste0("MLP_5_ASE")] = WindowedASE5
  results[i,paste0("MLP_6_ASE")] = WindowedASE6
  results[i,paste0("MLP_7_ASE")] = WindowedASE7
  results[i,paste0("MLP_8_ASE")] = WindowedASE8
  results[i,paste0("MLP_9_ASE")] = WindowedASE9
  results[i,paste0("MLP_10_ASE")] = WindowedASE10
  results[i,paste0("MLP_11_ASE")] = WindowedASE11
  results[i,paste0("MLP_12_ASE")] = WindowedASE12
  results[i,paste0("MLP_F1")] = forecasts$forecast[1]  
  results[i,paste0("MLP_F2")] = forecasts$forecast[2]   
  results[i,paste0("MLP_F3")] = forecasts$forecast[3]   
  results[i,paste0("MLP_F4")] = forecasts$forecast[4]   
  results[i,paste0("MLP_F5")] = forecasts$forecast[5]   
  results[i,paste0("MLP_F6")] = forecasts$forecast[6]   
  results[i,paste0("MLP_F7")] = forecasts$forecast[7]   
  results[i,paste0("MLP_F8")] = forecasts$forecast[8]   
  results[i,paste0("MLP_F9")] = forecasts$forecast[9]   
  results[i,paste0("MLP_F10")] = forecasts$forecast[10]   
  results[i,paste0("MLP_F11")] = forecasts$forecast[11]   
  results[i,paste0("MLP_F12")] = forecasts$forecast[12]   

  
  results[i,paste0("ACTUAL_1")] = temp1$STD_Cases[73]
  results[i,paste0("ACTUAL_2")] = temp1$STD_Cases[74]
  results[i,paste0("ACTUAL_3")] = temp1$STD_Cases[75]
  results[i,paste0("ACTUAL_4")] = temp1$STD_Cases[76]
  results[i,paste0("ACTUAL_5")] = temp1$STD_Cases[77]
  results[i,paste0("ACTUAL_6")] = temp1$STD_Cases[78]
  results[i,paste0("ACTUAL_7")] = temp1$STD_Cases[79]
  results[i,paste0("ACTUAL_8")] = temp1$STD_Cases[80]
  results[i,paste0("ACTUAL_9")] = temp1$STD_Cases[81]
  results[i,paste0("ACTUAL_10")] = temp1$STD_Cases[82]
  results[i,paste0("ACTUAL_11")] = temp1$STD_Cases[83]
  results[i,paste0("ACTUAL_12")] = temp1$STD_Cases[84]

  
  #graph ASEs for each Model
  EqualMeans_Results <- rbind(EqualMeans_Results_1,EqualMeans_Results_2,EqualMeans_Results_3,EqualMeans_Results_4,EqualMeans_Results_5,EqualMeans_Results_6,
                              EqualMeans_Results_7,EqualMeans_Results_8,EqualMeans_Results_9,EqualMeans_Results_10,EqualMeans_Results_11,EqualMeans_Results_12,
                              EqualMeans_Results_13)
  
  AR_Results <- rbind(AR_Results_1,AR_Results_2,AR_Results_3,AR_Results_4,AR_Results_5,AR_Results_6,AR_Results_7,AR_Results_8,AR_Results_9,AR_Results_10,
                      AR_Results_11,AR_Results_12,AR_Results_13)
  
  ARMA_Results <- rbind(ARMA_Results_1,ARMA_Results_2,ARMA_Results_3,ARMA_Results_4,ARMA_Results_5,ARMA_Results_6,ARMA_Results_7,ARMA_Results_8,
                       ARMA_Results_9,ARMA_Results_10,ARMA_Results_11,ARMA_Results_12,ARMA_Results_13)

  ARI_Results <- rbind(ARI_Results_1,ARI_Results_2,ARI_Results_3,ARI_Results_4,ARI_Results_5,ARI_Results_6,ARI_Results_7,ARI_Results_8,
                         ARI_Results_9,ARI_Results_10,ARI_Results_11,ARI_Results_12,ARI_Results_13)
 
  ARIMA_Results <- rbind(ARIMA_Results_1,ARIMA_Results_2,ARIMA_Results_3,ARIMA_Results_4,ARIMA_Results_5,ARIMA_Results_6,ARIMA_Results_7,ARIMA_Results_8,
                         ARIMA_Results_9,ARIMA_Results_10,ARIMA_Results_11,ARIMA_Results_12,ARIMA_Results_13)
      
  ARIS_Results <- rbind(ARIS_Results_1,ARIS_Results_2,ARIS_Results_3,ARIS_Results_4,ARIS_Results_5,ARIS_Results_6,ARIS_Results_7,ARIS_Results_8,
                          ARIS_Results_9,ARIS_Results_10,ARIS_Results_11,ARIS_Results_12,ARIS_Results_13)
  
  ARIMAS_Results <- rbind(ARIMAS_Results_1,ARIMAS_Results_2,ARIMAS_Results_3,ARIMAS_Results_4,ARIMAS_Results_5,ARIMAS_Results_6,ARIMAS_Results_7,ARIMAS_Results_8,
                          ARIMAS_Results_9,ARIMAS_Results_10,ARIMAS_Results_11,ARIMAS_Results_12,ARIMAS_Results_13)
  
  RF_Results <- rbind(RF_Results_1,RF_Results_2,RF_Results_3,RF_Results_4,RF_Results_5,RF_Results_6,RF_Results_7,RF_Results_8,
                        RF_Results_9,RF_Results_10,RF_Results_11,RF_Results_12,RF_Results_13)
    
  MLP_Results <- rbind(MLP_Results_1,MLP_Results_2,MLP_Results_3,MLP_Results_4,MLP_Results_5,MLP_Results_6,MLP_Results_7,MLP_Results_8,
                      MLP_Results_9,MLP_Results_10,MLP_Results_11,MLP_Results_12,MLP_Results_13)
      
  EqualMeans_Means <- colMeans(EqualMeans_Results)
  AR_Means <- colMeans(AR_Results)
  ARMA_Means <- colMeans(ARMA_Results)
  ARI_Means <- colMeans(ARI_Results)
  ARIMA_Means <- colMeans(ARIMA_Results)
  ARIS_Means <- colMeans(ARIS_Results)
  ARIMAS_Means <- colMeans(ARIMAS_Results)
  RF_Means <- colMeans(RF_Results)
  MLP_Means <- colMeans(MLP_Results)
  Combined_Means <- data.frame(EqualMeans_Means,AR_Means, ARMA_Means, ARI_Means, ARIMA_Means, ARIS_Means, ARIMAS_Means,RF_Means,MLP_Means)
  Combined_Means$horizon <- as.numeric(row.names(Combined_Means))
  
# more colors #73EBAE
  g <- ggplot(data=Combined_Means, aes(horizon)) +
    geom_line(aes(y=EqualMeans_Means, color="Equal Means"),size=1.5) +
    geom_line(aes(y=AR_Means, color="AR"),size=1.5) +
    geom_line(aes(y=ARMA_Means, color="ARMA"),size=1.5) +
    geom_line(aes(y=ARI_Means, color="AR with d=1"),size=1.5) +
    geom_line(aes(y=ARIMA_Means, color="ARIMA with d=1"),size=1.5) +
    geom_line(aes(y=ARIS_Means, color="AR with s=12"),size=1.5) +
    geom_line(aes(y=ARIMAS_Means, color="ARIMA with d=0, s=12"),size=1.5) +
    geom_line(aes(y=RF_Means, color="Random Forest"),size=1.5) +
    geom_line(aes(y=MLP_Means, color="MLP"),size=1.5) +
    scale_color_manual(values = c(
      'Equal Means' = '#004159',
      'AR' = '#65A8C4',
      'ARMA' = '#8C65D3',
      'AR with d=1' = '#9A93EC',
      'ARIMA with d=1' = '#0052A5',
      'AR with s=12' = '#413BF7',
      'ARIMA with d=0, s=12' = '#00ADCE',
      'Random Forest' = '#59DBF1',
      'MLP' = '#00C590'
    )) +
    labs(color='Models') +
    scale_x_continuous(breaks=seq(0,13,1)) +
    ggtitle(paste("Model ASEs for ", product,"and Customer",customer)) +
    xlab("Month Ahead Forecast") +
    ylab("ASE") +
    theme(panel.background = element_blank(), axis.line = element_line(colour = "black"), legend.title = element_blank())
  
  print(g)
  
# f-statistic calculations
    EqualMeans_DF <- rbind(EqualMeans_DF_1,EqualMeans_DF_2,EqualMeans_DF_3,EqualMeans_DF_4,EqualMeans_DF_5,EqualMeans_DF_6,EqualMeans_DF_7,
                           EqualMeans_DF_8,EqualMeans_DF_9,EqualMeans_DF_10,EqualMeans_DF_11,EqualMeans_DF_12,EqualMeans_DF_13)
    
    AR_DF <- rbind(AR_DF_1,AR_DF_2,AR_DF_3,AR_DF_4,AR_DF_5,AR_DF_6,AR_DF_7,AR_DF_8,AR_DF_9,AR_DF_10,AR_DF_11,AR_DF_12,AR_DF_13)
    
    ARI_DF <- rbind(ARI_DF_1,ARI_DF_2,ARI_DF_3,ARI_DF_4,ARI_DF_5,ARI_DF_6,ARI_DF_7,ARI_DF_8,ARI_DF_9,ARI_DF_10,ARI_DF_11,ARI_DF_12,ARI_DF_13)
    
    ARIS_DF <- rbind(ARIS_DF_1,ARIS_DF_2,ARIS_DF_3,ARIS_DF_4,ARIS_DF_5,ARIS_DF_6,ARIS_DF_7,ARIS_DF_8,ARIS_DF_9,ARIS_DF_10,ARIS_DF_11,ARIS_DF_12,ARIS_DF_13)
    
    
    EqualMeans_Results <- rbind(sum(EqualMeans_Results_1),sum(EqualMeans_Results_2),sum(EqualMeans_Results_3),sum(EqualMeans_Results_4),sum(EqualMeans_Results_5),
                                sum(EqualMeans_Results_6),sum(EqualMeans_Results_7),sum(EqualMeans_Results_8),sum(EqualMeans_Results_9),sum(EqualMeans_Results_10),
                                sum(EqualMeans_Results_11),sum(EqualMeans_Results_12),sum(EqualMeans_Results_13))
    
    AR_Results <- rbind(sum(AR_Results_1),sum(AR_Results_2),sum(AR_Results_3),sum(AR_Results_4),sum(AR_Results_5),sum(AR_Results_6),sum(AR_Results_7),
                        sum(AR_Results_8),sum(AR_Results_9),sum(AR_Results_10),sum(AR_Results_11),sum(AR_Results_12),sum(AR_Results_13))
    
    ARI_Results <- rbind(sum(ARI_Results_1),sum(ARI_Results_2),sum(ARI_Results_3),sum(ARI_Results_4),sum(ARI_Results_5),sum(ARI_Results_6),sum(ARI_Results_7),
                         sum(ARI_Results_8),sum(ARI_Results_9),sum(ARI_Results_10),sum(ARI_Results_11),sum(ARI_Results_12),sum(ARI_Results_13))
    
    ARIS_Results <- rbind(sum(ARIS_Results_1),sum(ARIS_Results_2),sum(ARIS_Results_3),sum(ARIS_Results_4),sum(ARIS_Results_5),sum(ARIS_Results_6),sum(ARIS_Results_7),
                         sum(ARIS_Results_8),sum(ARIS_Results_9),sum(ARIS_Results_10),sum(ARIS_Results_11),sum(ARIS_Results_12),sum(ARIS_Results_13))
    
    df_model = EqualMeans_DF - AR_DF
    ss_model = EqualMeans_Results - AR_Results
    ms_model = ss_model/df_model
    ms_ar = AR_Results/AR_DF
    F = ms_model/ms_ar
    AR_p_value = pf(F,df_model,AR_DF,lower.tail=FALSE)
    AR_p_tally = sum(AR_p_value[,1]<.05, na.rm=TRUE)
    results[i,"AR_F_Tally"] = AR_p_tally
    
    if (AR_p_tally >= 9){
      results[i,"AR_F_Conclusion"] = "Different"
    } else if (AR_p_tally <= 4){
      results[i,"AR_F_Conclusion"] = "Same"
    } else {
       results[i,"AR_F_Conclusion"] = "Inconclusive"
    }

    df_model = EqualMeans_DF - ARI_DF
    ss_model = EqualMeans_Results - ARI_Results
    ms_model = ss_model/df_model
    ms_ari = ARI_Results/ARI_DF
    F = ms_model/ms_ari
    ARI_p_value = pf(F,df_model,ARI_DF,lower.tail=FALSE)
    ARI_p_tally = sum(ARI_p_value[,1]<.05, na.rm=TRUE)
    results[i,"ARI_F_Tally"] = ARI_p_tally
    
    if (ARI_p_tally >= 9){
      results[i,"ARI_F_Conclusion"] = "Different"
    } else if (ARI_p_tally <= 4){
      results[i,"ARI_F_Conclusion"] = "Same"
    } else {
      results[i,"ARI_F_Conclusion"] = "Inconclusive"
    }
 
    df_model = EqualMeans_DF - ARIS_DF
    ss_model = EqualMeans_Results - ARIS_Results
    ms_model = ss_model/df_model
    ms_aris = ARIS_Results/ARIS_DF
    F = ms_model/ms_aris
    ARIS_p_value = pf(F,df_model,ARIS_DF,lower.tail=FALSE)
    ARIS_p_tally = sum(ARIS_p_value[,1]<.05, na.rm=TRUE)
    results[i,"ARIS_F_Tally"] = ARIS_p_tally
    
    if (ARIS_p_tally >= 9){
      results[i,"ARIS_F_Conclusion"] = "Different"
    } else if (ARIS_p_tally <= 4){
      results[i,"ARIS_F_Conclusion"] = "Same"
    } else {
       results[i,"ARIS_F_Conclusion"] = "Inconclusive"
    }

}

The Ljung-Box test with K=10 has a p-value of 0.002322024 .The Ljung-Box test with K=24 has a p-value of 0.0034262 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise."
[1] "Both tests for stationarity were inconclusive."

The Ljung-Box test with K=10 has a p-value of 0.007674533 .The Ljung-Box test with K=24 has a p-value of 0 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise."
[1] "Both stationarity tests indicate this time series is stationary."

The Ljung-Box test with K=10 has a p-value of 1.18705e-12 .The Ljung-Box test with K=24 has a p-value of 1.573741e-12 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both stationarity tests indicate this time series is NOT stationary."

The Ljung-Box test with K=10 has a p-value of 0.006130321 .The Ljung-Box test with K=24 has a p-value of 0.03101856 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both tests for stationarity were inconclusive."

The Ljung-Box test with K=10 has a p-value of 0.2367016 .The Ljung-Box test with K=24 has a p-value of 0.122692 .[1] "Ljung-Box test results: At a significance level of 0.05, we fail to reject the null hypothesis that this dataset is white noise."
[1] "One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise."
[1] "Both stationarity tests indicate this time series is stationary."

The Ljung-Box test with K=10 has a p-value of 9.303002e-10 .The Ljung-Box test with K=24 has a p-value of 1.985955e-07 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both stationarity tests indicate this time series is NOT stationary."

The Ljung-Box test with K=10 has a p-value of 0.004701657 .The Ljung-Box test with K=24 has a p-value of 0.232411 .[1] "Ljung-Box test results: At a significance level of 0.05, the test is inconclusive."
[1] "One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise."
[1] "Both tests for stationarity were inconclusive."

The Ljung-Box test with K=10 has a p-value of 0 .The Ljung-Box test with K=24 has a p-value of 0 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both stationarity tests indicate this time series is NOT stationary."

The Ljung-Box test with K=10 has a p-value of 0.02343884 .The Ljung-Box test with K=24 has a p-value of 0.1671774 .[1] "Ljung-Box test results: At a significance level of 0.05, the test is inconclusive."
[1] "One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise."
[1] "Both stationarity tests indicate this time series is NOT stationary."

The Ljung-Box test with K=10 has a p-value of 0 .The Ljung-Box test with K=24 has a p-value of 0 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both tests for stationarity were inconclusive."

The Ljung-Box test with K=10 has a p-value of 0.7619964 .The Ljung-Box test with K=24 has a p-value of 0.5395173 .[1] "Ljung-Box test results: At a significance level of 0.05, we fail to reject the null hypothesis that this dataset is white noise."
[1] "One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise."
[1] "Both tests for stationarity were inconclusive."

The Ljung-Box test with K=10 has a p-value of 3.036074e-07 .The Ljung-Box test with K=24 has a p-value of 1.098736e-05 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both tests for stationarity were inconclusive."

The Ljung-Box test with K=10 has a p-value of 0.1572929 .The Ljung-Box test with K=24 has a p-value of 0.3914269 .[1] "Ljung-Box test results: At a significance level of 0.05, we fail to reject the null hypothesis that this dataset is white noise."
[1] "One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise."
[1] "Both tests for stationarity were inconclusive."

The Ljung-Box test with K=10 has a p-value of 0 .The Ljung-Box test with K=24 has a p-value of 0 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both stationarity tests indicate this time series is NOT stationary."

The Ljung-Box test with K=10 has a p-value of 0 .The Ljung-Box test with K=24 has a p-value of 0 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both stationarity tests indicate this time series is NOT stationary."

The Ljung-Box test with K=10 has a p-value of 0.3857241 .The Ljung-Box test with K=24 has a p-value of 0.7674317 .[1] "Ljung-Box test results: At a significance level of 0.05, we fail to reject the null hypothesis that this dataset is white noise."
[1] "One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise."
[1] "Both tests for stationarity were inconclusive."

The Ljung-Box test with K=10 has a p-value of 2.798171e-05 .The Ljung-Box test with K=24 has a p-value of 0.0008768368 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both stationarity tests indicate this time series is NOT stationary."

The Ljung-Box test with K=10 has a p-value of 3.111778e-09 .The Ljung-Box test with K=24 has a p-value of 1.111885e-09 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both tests for stationarity were inconclusive."

The Ljung-Box test with K=10 has a p-value of 6.819545e-12 .The Ljung-Box test with K=24 has a p-value of 7.58651e-10 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both stationarity tests indicate this time series is NOT stationary."

The Ljung-Box test with K=10 has a p-value of 9.048454e-08 .The Ljung-Box test with K=24 has a p-value of 5.283449e-07 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both stationarity tests indicate this time series is NOT stationary."

The Ljung-Box test with K=10 has a p-value of 0.0009021729 .The Ljung-Box test with K=24 has a p-value of 0.01759268 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both stationarity tests indicate this time series is stationary."

The Ljung-Box test with K=10 has a p-value of 0 .The Ljung-Box test with K=24 has a p-value of 1.110223e-16 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both stationarity tests indicate this time series is NOT stationary."

The Ljung-Box test with K=10 has a p-value of 0 .The Ljung-Box test with K=24 has a p-value of 0 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both stationarity tests indicate this time series is NOT stationary."

The Ljung-Box test with K=10 has a p-value of 0.0739774 .The Ljung-Box test with K=24 has a p-value of 0.1020833 .[1] "Ljung-Box test results: At a significance level of 0.05, we fail to reject the null hypothesis that this dataset is white noise."
[1] "One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise."
[1] "Both stationarity tests indicate this time series is stationary."

The Ljung-Box test with K=10 has a p-value of 0 .The Ljung-Box test with K=24 has a p-value of 0 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both tests for stationarity were inconclusive."

The Ljung-Box test with K=10 has a p-value of 0.1224362 .The Ljung-Box test with K=24 has a p-value of 0.4792812 .[1] "Ljung-Box test results: At a significance level of 0.05, we fail to reject the null hypothesis that this dataset is white noise."
[1] "One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise."
[1] "Both stationarity tests indicate this time series is NOT stationary."

The Ljung-Box test with K=10 has a p-value of 0 .The Ljung-Box test with K=24 has a p-value of 0 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both tests for stationarity were inconclusive."

The Ljung-Box test with K=10 has a p-value of 0 .The Ljung-Box test with K=24 has a p-value of 0 .[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
[1] "Both tests for stationarity were inconclusive."

The Ljung-Box test with K=10 has a p-value of 0.1225766 .The Ljung-Box test with K=24 has a p-value of 0.5601297 .[1] "Ljung-Box test results: At a significance level of 0.05, we fail to reject the null hypothesis that this dataset is white noise."
[1] "One of the top 5 models using BIC was an ARMA(0,0), indicating this series may be white noise."
[1] "Both stationarity tests indicate this time series is NOT stationary."

results$winning_1 <- colnames(results[c("EqualMeans_1_ASE","AR_1_ASE","ARMA_1_ASE","ARI_1_ASE","ARIMA_1_ASE","ARI_S12_1_ASE","ARIMA_S12_1_ASE","RF_1_ASE","MLP_1_ASE")])[apply(results[c("EqualMeans_1_ASE","AR_1_ASE","ARMA_1_ASE","ARI_1_ASE","ARIMA_1_ASE","ARI_S12_1_ASE","ARIMA_S12_1_ASE","RF_1_ASE","MLP_1_ASE")],1,which.min)]

results$winning_2 <- colnames(results[c("EqualMeans_2_ASE","AR_2_ASE","ARMA_2_ASE","ARI_2_ASE","ARIMA_2_ASE","ARI_S12_2_ASE","ARIMA_S12_2_ASE","RF_2_ASE","MLP_2_ASE")])[apply(results[c("EqualMeans_2_ASE","AR_2_ASE","ARMA_2_ASE","ARI_2_ASE","ARIMA_2_ASE","ARI_S12_2_ASE","ARIMA_S12_2_ASE","RF_2_ASE","MLP_2_ASE")],1,which.min)]

results$winning_3 <- colnames(results[c("EqualMeans_3_ASE","AR_3_ASE","ARMA_3_ASE","ARI_3_ASE","ARIMA_3_ASE","ARI_S12_3_ASE","ARIMA_S12_3_ASE","RF_3_ASE","MLP_3_ASE")])[apply(results[c("EqualMeans_3_ASE","AR_3_ASE","ARMA_3_ASE","ARI_3_ASE","ARIMA_3_ASE","ARI_S12_3_ASE","ARIMA_S12_3_ASE","RF_3_ASE","MLP_3_ASE")],1,which.min)]

results$winning_4 <- colnames(results[c("EqualMeans_4_ASE","AR_4_ASE","ARMA_4_ASE","ARI_4_ASE","ARIMA_4_ASE","ARI_S12_4_ASE","ARIMA_S12_4_ASE","RF_4_ASE","MLP_4_ASE")])[apply(results[c("EqualMeans_4_ASE","AR_4_ASE","ARMA_4_ASE","ARI_4_ASE","ARIMA_4_ASE","ARI_S12_4_ASE","ARIMA_S12_4_ASE","RF_4_ASE","MLP_4_ASE")],1,which.min)]

results$winning_5 <- colnames(results[c("EqualMeans_5_ASE","AR_5_ASE","ARMA_5_ASE","ARI_5_ASE","ARIMA_5_ASE","ARI_S12_5_ASE","ARIMA_S12_5_ASE","RF_5_ASE","MLP_5_ASE")])[apply(results[c("EqualMeans_5_ASE","AR_5_ASE","ARMA_5_ASE","ARI_5_ASE","ARIMA_5_ASE","ARI_S12_5_ASE","ARIMA_S12_5_ASE","RF_5_ASE","MLP_5_ASE")],1,which.min)]

results$winning_6 <- colnames(results[c("EqualMeans_6_ASE","AR_6_ASE","ARMA_6_ASE","ARI_6_ASE","ARIMA_6_ASE","ARI_S12_6_ASE","ARIMA_S12_6_ASE","RF_6_ASE","MLP_6_ASE")])[apply(results[c("EqualMeans_6_ASE","AR_6_ASE","ARMA_6_ASE","ARI_6_ASE","ARIMA_6_ASE","ARI_S12_6_ASE","ARIMA_S12_6_ASE","RF_6_ASE","MLP_6_ASE")],1,which.min)]

results$winning_7 <- colnames(results[c("EqualMeans_7_ASE","AR_7_ASE","ARMA_7_ASE","ARI_7_ASE","ARIMA_7_ASE","ARI_S12_7_ASE","ARIMA_S12_7_ASE","RF_7_ASE","MLP_7_ASE")])[apply(results[c("EqualMeans_7_ASE","AR_7_ASE","ARMA_7_ASE","ARI_7_ASE","ARIMA_7_ASE","ARI_S12_7_ASE","ARIMA_S12_7_ASE","RF_7_ASE","MLP_7_ASE")],1,which.min)]

results$winning_8 <- colnames(results[c("EqualMeans_8_ASE","AR_8_ASE","ARMA_8_ASE","ARI_8_ASE","ARIMA_8_ASE","ARI_S12_8_ASE","ARIMA_S12_8_ASE","RF_8_ASE","MLP_8_ASE")])[apply(results[c("EqualMeans_8_ASE","AR_8_ASE","ARMA_8_ASE","ARI_8_ASE","ARIMA_8_ASE","ARI_S12_8_ASE","ARIMA_S12_8_ASE","RF_8_ASE","MLP_8_ASE")],1,which.min)]

results$winning_9 <- colnames(results[c("EqualMeans_9_ASE","AR_9_ASE","ARMA_9_ASE","ARI_9_ASE","ARIMA_9_ASE","ARI_S12_9_ASE","ARIMA_S12_9_ASE","RF_9_ASE","MLP_9_ASE")])[apply(results[c("EqualMeans_9_ASE","AR_9_ASE","ARMA_9_ASE","ARI_9_ASE","ARIMA_9_ASE","ARI_S12_9_ASE","ARIMA_S12_9_ASE","RF_9_ASE","MLP_9_ASE")],1,which.min)]

results$winning_10 <- colnames(results[c("EqualMeans_10_ASE","AR_10_ASE","ARMA_10_ASE","ARI_10_ASE","ARIMA_10_ASE","ARI_S12_10_ASE","ARIMA_S12_10_ASE","RF_10_ASE","MLP_10_ASE")])[apply(results[c("EqualMeans_10_ASE","AR_10_ASE","ARMA_10_ASE","ARI_10_ASE","ARIMA_10_ASE","ARI_S12_10_ASE","ARIMA_S12_10_ASE","RF_10_ASE","MLP_10_ASE")],1,which.min)]

results$winning_11 <- colnames(results[c("EqualMeans_11_ASE","AR_11_ASE","ARMA_11_ASE","ARI_11_ASE","ARIMA_11_ASE","ARI_S12_11_ASE","ARIMA_S12_11_ASE","RF_11_ASE","MLP_11_ASE")])[apply(results[c("EqualMeans_11_ASE","AR_11_ASE","ARMA_11_ASE","ARI_11_ASE","ARIMA_11_ASE","ARI_S12_11_ASE","ARIMA_S12_11_ASE","RF_11_ASE","MLP_11_ASE")],1,which.min)]

results$winning_12 <- colnames(results[c("EqualMeans_12_ASE","AR_12_ASE","ARMA_12_ASE","ARI_12_ASE","ARIMA_12_ASE","ARI_S12_12_ASE","ARIMA_S12_12_ASE","RF_12_ASE","MLP_12_ASE")])[apply(results[c("EqualMeans_12_ASE","AR_12_ASE","ARMA_12_ASE","ARI_12_ASE","ARIMA_12_ASE","ARI_S12_12_ASE","ARIMA_S12_12_ASE","RF_12_ASE","MLP_12_ASE")],1,which.min)]

formattable(results, align = c("l", rep("r", NCOL(table_a) - 1)))
Product_Type Product Customer ljung_10 ljung_24 ljung_results top_5_bic ADF KPSS stationarity_results EqualMeans_1_ASE EqualMeans_2_ASE EqualMeans_3_ASE EqualMeans_4_ASE EqualMeans_5_ASE EqualMeans_6_ASE EqualMeans_7_ASE EqualMeans_8_ASE EqualMeans_9_ASE EqualMeans_10_ASE EqualMeans_11_ASE EqualMeans_12_ASE EqualMeans_F1 EqualMeans_F2 EqualMeans_F3 EqualMeans_F4 EqualMeans_F5 EqualMeans_F6 EqualMeans_F7 EqualMeans_F8 EqualMeans_F9 EqualMeans_F10 EqualMeans_F11 EqualMeans_F12 AR_1_ASE AR_2_ASE AR_3_ASE AR_4_ASE AR_5_ASE AR_6_ASE AR_7_ASE AR_8_ASE AR_9_ASE AR_10_ASE AR_11_ASE AR_12_ASE AR_F1 AR_F2 AR_F3 AR_F4 AR_F5 AR_F6 AR_F7 AR_F8 AR_F9 AR_F10 AR_F11 AR_F12 ARMA_1_ASE ARMA_2_ASE ARMA_3_ASE ARMA_4_ASE ARMA_5_ASE ARMA_6_ASE ARMA_7_ASE ARMA_8_ASE ARMA_9_ASE ARMA_10_ASE ARMA_11_ASE ARMA_12_ASE ARMA_F1 ARMA_F2 ARMA_F3 ARMA_F4 ARMA_F5 ARMA_F6 ARMA_F7 ARMA_F8 ARMA_F9 ARMA_F10 ARMA_F11 ARMA_F12 ARI_1_ASE ARI_2_ASE ARI_3_ASE ARI_4_ASE ARI_5_ASE ARI_6_ASE ARI_7_ASE ARI_8_ASE ARI_9_ASE ARI_10_ASE ARI_11_ASE ARI_12_ASE ARI_F1 ARI_F2 ARI_F3 ARI_F4 ARI_F5 ARI_F6 ARI_F7 ARI_F8 ARI_F9 ARI_F10 ARI_F11 ARI_F12 ARIMA_1_ASE ARIMA_2_ASE ARIMA_3_ASE ARIMA_4_ASE ARIMA_5_ASE ARIMA_6_ASE ARIMA_7_ASE ARIMA_8_ASE ARIMA_9_ASE ARIMA_10_ASE ARIMA_11_ASE ARIMA_12_ASE ARIMA_F1 ARIMA_F2 ARIMA_F3 ARIMA_F4 ARIMA_F5 ARIMA_F6 ARIMA_F7 ARIMA_F8 ARIMA_F9 ARIMA_F10 ARIMA_F11 ARIMA_F12 ARI_S12_1_ASE ARI_S12_2_ASE ARI_S12_3_ASE ARI_S12_4_ASE ARI_S12_5_ASE ARI_S12_6_ASE ARI_S12_7_ASE ARI_S12_8_ASE ARI_S12_9_ASE ARI_S12_10_ASE ARI_S12_11_ASE ARI_S12_12_ASE ARI_S12_F1 ARI_S12_F2 ARI_S12_F3 ARI_S12_F4 ARI_S12_F5 ARI_S12_F6 ARI_S12_F7 ARI_S12_F8 ARI_S12_F9 ARI_S12_F10 ARI_S12_F11 ARI_S12_F12 ARIMA_S12_1_ASE ARIMA_S12_2_ASE ARIMA_S12_3_ASE ARIMA_S12_4_ASE ARIMA_S12_5_ASE ARIMA_S12_6_ASE ARIMA_S12_7_ASE ARIMA_S12_8_ASE ARIMA_S12_9_ASE ARIMA_S12_10_ASE ARIMA_S12_11_ASE ARIMA_S12_12_ASE ARIMA_S12_F1 ARIMA_S12_F2 ARIMA_S12_F3 ARIMA_S12_F4 ARIMA_S12_F5 ARIMA_S12_F6 ARIMA_S12_F7 ARIMA_S12_F8 ARIMA_S12_F9 ARIMA_S12_F10 ARIMA_S12_F11 ARIMA_S12_F12 RF_1_ASE RF_2_ASE RF_3_ASE RF_4_ASE RF_5_ASE RF_6_ASE RF_7_ASE RF_8_ASE RF_9_ASE RF_10_ASE RF_11_ASE RF_12_ASE RF_F1 RF_F2 RF_F3 RF_F4 RF_F5 RF_F6 RF_F7 RF_F8 RF_F9 RF_F10 RF_F11 RF_F12 MLP_1_ASE MLP_2_ASE MLP_3_ASE MLP_4_ASE MLP_5_ASE MLP_6_ASE MLP_7_ASE MLP_8_ASE MLP_9_ASE MLP_10_ASE MLP_11_ASE MLP_12_ASE MLP_F1 MLP_F2 MLP_F3 MLP_F4 MLP_F5 MLP_F6 MLP_F7 MLP_F8 MLP_F9 MLP_F10 MLP_F11 MLP_F12 ACTUAL_1 ACTUAL_2 ACTUAL_3 ACTUAL_4 ACTUAL_5 ACTUAL_6 ACTUAL_7 ACTUAL_8 ACTUAL_9 ACTUAL_10 ACTUAL_11 ACTUAL_12 AR_F_Tally AR_F_Conclusion ARI_F_Tally ARI_F_Conclusion ARIS_F_Tally ARIS_F_Conclusion winning_1 winning_2 winning_3 winning_4 winning_5 winning_6 winning_7 winning_8 winning_9 winning_10 winning_11 winning_12
700005925 TAAKA VODKA 80 1L 700005925 2.322024e-03 3.426200e-03 not white noise white noise 0.16051598 0.08236679 inconclusive 819.7760806 812.0658241 815.1706105 689.8962088 601.4447370 535.9172216 489.1170549 453.3300453 418.8453911 390.5514370 364.9275910 346.4278690 51.2200000 51.2200000 51.2200000 51.2200000 51.2200000 51.2200000 51.2200000 51.2200000 51.2200000 51.2200000 51.2200000 51.2200000 1177.6244193 978.5196647 902.4422639 751.9989173 645.2789428 571.7912574 518.0486590 477.8120609 439.9488641 409.2232404 381.7398073 361.6837778 56.4915307 52.0502457 52.7957777 52.6563411 51.7062837 51.9118351 51.6557065 51.4741287 51.4785061 51.3733314 51.3337370 51.3135431 1220.5831606 1064.5110370 1020.3968276 830.2558671 695.6295191 611.3732866 546.3263424 504.5024731 459.2102364 428.8023578 399.9887614 380.7868738 53.2174811 53.1162966 56.4704512 49.4069529 54.6932876 51.3134915 52.7815933 52.1860505 51.1159264 52.8831414 50.7506623 52.3671199 1214.2332055 1015.2921504 938.4920537 808.0033204 686.8916915 639.1105693 577.9161054 536.2514127 505.2446771 472.0050923 449.2638583 426.9739251 60.845915 49.4615997 62.0138866 52.3476761 55.7535902 57.6035076 53.3478106 58.2313454 53.7935218 56.5314612 56.1117596 54.8232972 1.019355e+03 922.8713034 881.9550582 728.1959511 631.0542952 564.5865050 514.4789610 473.0086187 442.0050082 409.5462412 383.0871323 361.6927564 43.2661616 49.3228573 45.0704739 48.2247324 45.8328942 47.6618459 46.2589500 47.3362781 46.5086135 47.1445714 46.6558885 47.0314102 893.8762186 814.9139459 889.4334274 878.0046680 820.6963147 780.1064112 744.4318734 722.5259322 704.2269863 690.0382715 679.6170963 677.0644941 4.271114e+01 56.8988570 132.0143853 1.399795e+01 7.590029e+01 5.999996e+01 6.800001e+01 78.9999992 41.0000001 69.99999998 54.0000000 5.300000e+01 1057.5807655 1102.1703032 1124.8257798 1062.8228638 972.4991512 912.1410119 858.1841098 821.6447126 793.4708438 777.0434603 756.2249502 747.7752374 4.200000e+01 57.0000000 132.0000000 1.400000e+01 7.590000e+01 6.000000e+01 6.800000e+01 79.0000000 41.000000 70.00000000 54.000000 5.300000e+01 677.5376902 672.0302239 667.9522967 581.3353826 488.6867852 421.5943371 374.4843922 336.7191703 305.6265898 283.3723851 263.9415954 251.8716028 44.78000667 57.5735733 66.0851667 40.10861333 66.0851667 59.24699333 64.1085600 66.0851667 44.3042533 64.1678600 55.3119600 54.81204333 1626.7719316 1340.8483610 1290.1894880 1070.3831591 953.3553657 867.5341194 802.7019114 753.9624096 706.0567608 656.2031659 611.4135140 580.5781610 32.17810845 41.5492581 43.7429295 43.8813073 43.3119445 43.5997174 44.6649832 38.4759884 45.8302834 41.13984728 49.6347994 48.7468377 60 52.0 67 58 73 57 63.0 64.9 47.0 50 48 29.0 4 Same 9 Different 3 Same RF_1_ASE RF_2_ASE RF_3_ASE RF_4_ASE RF_5_ASE RF_6_ASE RF_7_ASE RF_8_ASE RF_9_ASE RF_10_ASE RF_11_ASE RF_12_ASE
701000317 TAAKA VODKA 80 1L 701000317 7.674533e-03 0.000000e+00 not white noise white noise 0.01000000 0.10000000 stationary 5386.0238675 5396.0610470 6184.2691667 5551.7975855 5173.2864316 4930.6700214 4762.6696551 4625.7466239 4532.8720157 4471.5482265 4408.0742172 4359.0114744 101.7833333 101.7833333 101.7833333 101.7833333 101.7833333 101.7833333 101.7833333 101.7833333 101.7833333 101.7833333 101.7833333 101.7833333 5035.1703107 5218.7360889 6067.1292134 5463.9904498 5103.1262789 4872.2197743 4712.5738354 4581.9131435 4493.9089720 4436.4814879 4376.1953620 4329.7891886 94.8965765 100.6204215 101.5869617 101.7501736 101.7777339 101.7823878 101.7831737 101.7833064 101.7833288 101.7833326 101.7833332 101.7833333 5075.7624303 5322.5093370 5872.8687369 5059.3211299 4602.3842109 4469.0630501 4407.4131580 4192.1642408 4009.6761962 3890.3554742 3842.3155123 3826.2041051 95.1469980 111.2239452 130.6665597 134.9830893 132.6160184 120.0699014 107.4203227 94.9279002 87.1687948 84.0405840 86.5048168 92.1487011 6607.0465449 7721.2289278 9528.0691323 9245.2105154 9221.0967129 9132.5798545 9014.7805722 8680.0288513 8219.4212424 7713.4636748 7195.1123577 6708.3364610 57.768599 48.5952996 50.8681015 53.8012251 53.8899160 52.1873256 52.2738219 52.8118326 52.9513696 52.6621260 52.6217593 52.7090493 1.067297e+04 8896.2364736 9681.2959002 7939.4196886 7844.4094248 7990.1810252 8554.5884303 8495.5687722 8648.9829702 8580.5019700 8400.6342571 8098.7569531 100.7928105 106.1108503 104.0874318 98.5400584 96.0526262 95.8392398 96.5603734 97.1166996 97.2837055 97.2210394 97.1236224 97.0748714 431.8207267 454.5782997 515.4262725 515.4481941 512.5350830 548.3198016 569.9995070 594.0760074 613.9132478 634.0917989 635.8335107 637.6881522 6.164025e+01 133.0261755 329.6865732 1.130957e+02 1.059708e+02 1.240089e+02 1.359973e+02 103.0008331 69.9997455 25.00007772 46.9999763 6.100001e+01 8433.3857923 5154.1237411 3763.1088122 2967.9427354 2477.4753201 2186.1939136 1971.8970771 1821.0071934 1703.7337292 1614.6880514 1527.2622155 1454.6370126 6.260246e+01 132.0000000 330.0000000 1.130000e+02 1.060000e+02 1.240000e+02 1.360000e+02 103.0000000 70.000000 25.00000000 47.000000 6.100000e+01 2009.2674629 2235.8452139 2347.1904314 2158.0062389 2107.9777941 2112.5452004 2147.9195318 2081.7304947 1988.3184262 1886.0493562 1794.2868689 1711.8133189 58.31030000 98.8225667 246.5644000 92.59386667 90.1950000 98.19896667 99.1769667 89.7599000 59.9459333 47.3314000 51.5643000 57.93950000 7302.8322258 6946.6753454 7817.3709866 6976.5648298 6350.9840361 5963.1064014 5749.2526523 5576.1605840 5461.4797738 5353.9654920 5242.6849756 5140.9396995 66.17634435 73.0283908 76.5870901 75.1246430 86.1783977 92.4855528 92.4855540 92.4855541 92.4855541 75.59315357 86.6490804 92.4855541 88 125.0 280 136 113 69 139.0 74.0 56.0 50 46 52.0 0 Same 0 Same 13 Different ARI_S12_1_ASE ARI_S12_2_ASE ARI_S12_3_ASE ARI_S12_4_ASE ARI_S12_5_ASE ARI_S12_6_ASE ARI_S12_7_ASE ARI_S12_8_ASE ARI_S12_9_ASE ARI_S12_10_ASE ARI_S12_11_ASE ARI_S12_12_ASE
701001770 TAAKA VODKA 80 1L 701001770 1.187050e-12 1.573741e-12 not white noise NA 0.53188120 0.01000000 not stationary 6037.8142344 6011.6269267 6006.4802173 5164.7525036 4552.7806959 4119.4096190 3804.3090329 3566.8000677 3361.0108897 3202.4520857 3057.9253719 2878.2446917 106.4600000 106.4600000 106.4600000 106.4600000 106.4600000 106.4600000 106.4600000 106.4600000 106.4600000 106.4600000 106.4600000 106.4600000 6488.5970271 6395.9339005 6521.3455398 5842.0743353 4867.8635968 4310.0105737 3868.3217124 3529.3701005 3233.2800040 3017.4922756 2848.6383501 2662.4500660 122.3825927 141.4522638 156.8207240 146.5400699 132.7953512 134.8241282 140.8787658 136.8375946 131.1094967 130.4689701 131.6987452 130.0852146 6069.9661721 5828.9569556 5547.8444068 4610.1606213 3791.3806203 3434.4124271 3067.2728007 2758.3131160 2544.1935701 2414.8295759 2316.1141232 2178.9429165 126.1569793 146.0084226 143.7054915 138.8871720 139.8964381 139.0296243 137.7483457 137.0800734 136.2793895 135.4398483 134.6801564 133.9294398 6965.6153532 7278.5744593 7251.8801768 6406.9688800 5337.7932017 4720.5019793 4240.2377469 3853.4744897 3581.0515812 3352.6918536 3201.0444177 3043.0077283 130.608397 149.5099179 167.8357808 158.6284493 146.5277043 151.2585751 159.1897122 156.5399797 151.7689753 152.9420884 155.9654258 155.4518223 5.254440e+03 4999.1257339 5154.8823639 4783.7655494 4074.9633382 3593.7634359 3216.2823825 2939.4821732 2754.5828734 2607.4836920 2519.5146881 2417.0835426 130.6083974 149.5099179 167.8357808 158.6284493 146.5277043 151.2585751 159.1897122 156.5399797 151.7689753 152.9420884 155.9654258 155.4518223 6105.4555197 5761.0267969 6212.9203410 5915.2780651 5626.1279553 5448.5127186 5299.6359268 5191.4314014 5091.0703660 5004.9910085 4973.3309083 4973.9199318 1.202644e+02 139.3387993 306.7948196 7.031445e+00 1.549952e+02 1.270007e+02 1.179999e+02 154.0000173 91.9999973 148.00000041 191.9999999 1.620000e+02 6366.8174714 6162.0168690 6965.4999529 6622.7382835 6228.5606941 6005.9191192 5770.7234801 5585.5098089 5469.6374123 5399.0224535 5393.4726932 5417.6119722 1.290000e+02 138.0000000 307.0000000 7.000000e+00 1.550000e+02 1.270000e+02 1.180000e+02 154.0000000 92.000000 148.00000000 192.000000 1.620000e+02 4476.2253472 4485.6273912 4539.9970884 3825.5443318 3204.6010793 2861.9519095 2649.6991122 2504.8517974 2371.5942488 2255.4476137 2197.0476437 2149.1009365 139.29516000 142.0430633 173.5373433 97.21386333 145.1196500 137.66300667 128.4414800 145.1196500 111.5212533 143.8662167 173.5373433 158.10345667 4773.2631881 4787.6204258 4801.1928451 4109.9659070 3505.4248915 3088.1662382 2816.1203786 2581.6061954 2383.8898748 2241.7188533 2116.6974659 1988.3585582 119.62106270 116.9377401 112.1221545 116.6896836 114.9349521 110.6252980 114.5338947 123.7486316 113.9088299 110.22667138 109.1751398 115.3994394 147 117.0 142 133 111 83 95.0 114.0 91.9 104 117 100.0 4 Same 5 Inconclusive 2 Same RF_1_ASE RF_2_ASE RF_3_ASE RF_4_ASE RF_5_ASE RF_6_ASE RF_7_ASE RF_8_ASE RF_9_ASE MLP_10_ASE MLP_11_ASE MLP_12_ASE
701001790 TAAKA VODKA 80 1L 701001790 6.130321e-03 3.101856e-02 not white noise NA 0.23862134 0.10000000 inconclusive 656.5598284 653.9191489 657.4544780 565.9303476 481.6666900 426.3206618 387.9143779 358.5476137 336.9679082 318.7005028 304.7056093 294.3995806 47.6116667 47.6116667 47.6116667 47.6116667 47.6116667 47.6116667 47.6116667 47.6116667 47.6116667 47.6116667 47.6116667 47.6116667 786.5930500 716.3372144 712.5096524 608.2918395 514.4203764 461.0356173 418.4398183 383.9446630 355.6715510 333.1692130 315.3258779 302.7288698 51.6172774 57.0747935 53.3426211 51.0867726 51.0975895 49.6858496 49.2853439 48.8737669 48.4875122 48.2957402 48.1040299 47.9758083 786.6821475 714.5797864 711.4097381 607.2602509 513.3486510 460.5636041 418.4143139 384.0363764 356.1047069 333.7082767 316.0337581 303.6017446 50.1138106 56.0235607 52.5582075 52.5577752 51.5403314 51.0307437 50.4769171 50.0500161 49.6736841 49.3599313 49.0923578 48.8662770 914.0287943 799.3570062 790.6682658 685.3500082 591.7141719 552.9409655 513.8854120 478.0154518 444.5616395 418.0618258 397.7465833 385.4888968 59.049900 65.6257614 64.5197884 63.1589165 64.7194735 63.8546948 64.0502566 64.1860772 64.0003658 64.1124673 64.0812833 64.0686986 8.578247e+02 740.6271509 750.6761298 646.1743870 547.8952825 502.9643017 458.7333820 422.7623404 390.8696895 368.0898651 352.1400245 344.3114579 52.6895755 58.3425279 56.6876771 57.1721197 57.0303035 57.0718189 57.0596657 57.0632234 57.0621819 57.0624868 57.0623976 57.0624237 780.8708943 718.2994717 809.5499929 808.6626919 758.7096754 727.8598668 707.9002126 694.1311879 681.0637345 670.4667210 666.5287772 676.1579899 6.789311e+01 55.1070490 119.9267300 6.368655e+00 5.489771e+01 5.193155e+01 5.440356e+01 55.3706734 35.1773121 54.14892463 59.0767145 7.206030e+01 842.6917713 898.1286013 959.1236222 904.9257325 814.4104498 774.4453964 743.4284306 731.9260579 714.1077562 702.2044549 696.7813044 699.6595046 6.789311e+01 55.1070490 119.9267300 6.368655e+00 5.489771e+01 5.193155e+01 5.440356e+01 55.3706734 35.177312 54.14892463 59.076715 7.206030e+01 578.1082136 575.6157280 570.7736948 516.3770639 435.4491186 384.7926711 351.7960350 326.9359670 308.4523974 292.0029125 283.2612056 281.5804943 58.73956667 50.5562667 60.4062333 33.87182000 54.6964667 52.23450000 54.6964667 55.6670667 37.2621967 54.6964667 57.8414000 60.40623333 596.4441001 536.3324039 555.1023137 484.9851129 407.6498666 355.2203243 322.6561843 298.2118689 280.9969834 267.3889590 256.6234448 252.9205554 56.44188977 50.0326353 53.9840618 39.7563976 46.2034752 53.2079140 44.0259732 48.3147209 50.3692325 50.74911637 48.2999796 51.0392556 63 64.9 59 55 52 39 35.0 44.0 32.0 40 33 28.9 1 Same 2 Same 0 Same RF_1_ASE MLP_2_ASE MLP_3_ASE MLP_4_ASE MLP_5_ASE MLP_6_ASE MLP_7_ASE MLP_8_ASE MLP_9_ASE MLP_10_ASE MLP_11_ASE MLP_12_ASE
700005448 TAAKA VODKA 80 1L 700005448 2.367016e-01 1.226920e-01 white noise white noise 0.01000000 0.10000000 stationary 3.2606182 3.2721566 3.2434387 3.0333105 2.7925156 2.5995498 2.4645339 2.3359643 2.2364786 2.1533002 2.0775063 2.0241096 2.7483333 2.7483333 2.7483333 2.7483333 2.7483333 2.7483333 2.7483333 2.7483333 2.7483333 2.7483333 2.7483333 2.7483333 3.3781013 3.3095393 3.2432368 3.0395011 2.7916400 2.5992903 2.4654883 2.3346686 2.2343802 2.1494476 2.0740426 2.0212109 2.7164817 2.7486453 2.7483303 2.7483334 2.7483333 2.7483333 2.7483333 2.7483333 2.7483333 2.7483333 2.7483333 2.7483333 3.3155536 3.6951052 3.5728124 3.2893304 2.9938501 2.7727916 2.6125905 2.4612121 2.3474646 2.2538158 2.1690031 2.1081807 2.7483333 2.7483333 2.7483333 2.7483333 2.7483333 2.7483333 2.7483333 2.7483333 2.7483333 2.7483333 2.7483333 2.7483333 4.8010660 4.6320358 4.8689421 4.7621693 4.5819942 4.3871059 4.1607583 3.9119798 3.6244150 3.3878035 3.2129862 3.1616146 4.523339 5.0464211 5.0789813 4.9065999 5.0246405 4.9863733 4.9811519 4.9958593 4.9864811 4.9892344 4.9898611 4.9886176 4.277557e+00 4.4170716 4.2540623 4.2082053 4.0010940 3.7620384 3.5477853 3.2918129 3.0336648 2.8995667 2.7235312 2.6498099 2.0911105 2.3396315 1.6856053 1.7126542 1.6028931 1.6049587 1.5864818 1.5864097 1.5832898 1.5832066 1.5826781 1.5826521 5.1842619 4.7438252 4.5576617 4.1595069 3.7585025 3.5397909 3.4232620 3.3414186 3.2281092 3.1148636 3.0208574 3.1073461 4.394872e+00 3.5629699 5.9933855 -6.026074e-01 8.879026e-01 3.114198e+00 9.120087e-01 3.1909435 2.0235236 3.96196530 4.0555991 5.935030e+00 5.2717011 4.8712880 4.5640162 4.1850058 3.8107385 3.6754518 3.5445104 3.4088147 3.2588620 3.1409703 3.0572035 3.1602990 4.394872e+00 3.5629699 5.9933855 -6.026074e-01 8.879026e-01 3.114198e+00 9.120087e-01 3.1909435 2.023524 3.96196530 4.055599 5.935030e+00 4.0592499 3.9412731 3.8647310 3.4190700 3.0436178 2.7799210 2.6067920 2.4927114 2.4094821 2.3236274 2.2344354 2.1987716 3.77810000 3.7781000 3.8581000 1.70382000 1.7106200 3.25950000 1.7106200 3.2595000 2.2603333 3.7781000 3.7781000 3.85810000 3.1024754 3.1418167 3.1181259 2.9214136 2.6844347 2.4922830 2.3633401 2.2417774 2.1527288 2.0768826 2.0087534 1.9643989 2.86720177 2.7836153 2.7939332 2.7990557 2.7986444 2.8004600 2.7985168 2.8005203 2.7985121 2.80052293 2.7985119 2.8005230 3 4.0 3 2 3 2 1.9 2.0 2.0 3 2 1.0 0 Same 0 Same 0 Same MLP_1_ASE MLP_2_ASE MLP_3_ASE MLP_4_ASE MLP_5_ASE MLP_6_ASE MLP_7_ASE MLP_8_ASE MLP_9_ASE MLP_10_ASE MLP_11_ASE MLP_12_ASE
700005910 TAAKA VODKA 80 1L 700005910 9.303002e-10 1.985955e-07 not white noise NA 0.41243058 0.01000000 not stationary 6.7172506 6.7250712 6.5282763 5.5460968 4.8189942 4.3354985 3.8306572 3.4450071 3.1375640 2.8975071 2.7124721 2.5533618 3.5983333 3.5983333 3.5983333 3.5983333 3.5983333 3.5983333 3.5983333 3.5983333 3.5983333 3.5983333 3.5983333 3.5983333 6.0858731 5.4317515 5.0313406 5.2157861 4.7147004 4.2545220 3.9106572 3.4979056 3.2110668 3.0507028 2.8893624 2.7371097 3.9108782 3.8589130 4.3650583 3.8193368 3.7658267 4.0203365 3.7464232 3.7050224 3.8320614 3.6942498 3.6657190 3.7285952 6.1013892 5.9203572 5.1397653 5.1470264 4.7179650 4.3067151 3.9056435 3.4903498 3.2598653 3.0606990 2.8924495 2.7913065 3.9108782 3.8589130 4.3650583 3.8193368 3.7658267 4.0203365 3.7464232 3.7050224 3.8320614 3.6942498 3.6657190 3.7285952 6.4180671 5.5822237 5.1910526 5.7611289 5.3900833 4.9376795 4.7755047 4.4630113 4.2442940 4.1784287 4.1535670 4.0361142 4.196913 4.1858766 4.7215529 4.2985980 4.2868719 4.5737411 4.3510523 4.3417089 4.4952930 4.3780807 4.3714635 4.4536672 6.418067e+00 5.5822237 5.1910526 5.7611289 5.3900833 4.9376795 4.7755047 4.4630113 4.2442940 4.1784287 4.1535670 4.0361142 4.1969130 4.1858766 4.7215529 4.2985980 4.2868719 4.5737411 4.3510523 4.3417089 4.4952930 4.3780807 4.3714635 4.4536672 4.9882098 4.6530860 5.2562434 5.5832256 5.6552794 5.8574158 6.0287645 6.1841193 6.3014406 6.3962147 6.5002135 6.5669629 2.474223e+00 5.2479551 9.2218859 -3.577969e-01 3.677761e+00 6.687046e+00 1.812916e+00 4.8541127 2.8693219 3.91063865 3.9330345 4.943742e+00 12.9033412 14.3702306 13.6094087 12.4329890 13.0086409 12.1494337 11.3515892 10.8322386 10.5849708 10.3442391 10.3014626 10.5715793 2.827593e+00 5.0647919 9.9032571 -2.211545e-01 3.837791e+00 7.005361e+00 1.897978e+00 5.0104979 2.971441 3.98968502 4.001390 4.989016e+00 4.5437145 4.5945908 4.6793982 4.0201394 3.5367639 3.3185032 3.0099518 2.8190769 2.6780813 2.5682226 2.5384174 2.4973166 3.99018333 6.0843000 6.2374667 3.44851000 5.4406333 6.23746667 3.5834433 5.9434333 3.9901833 5.4406333 5.4406333 5.94343333 6.4916416 6.7094167 6.6209159 5.6655419 4.9489381 4.4628948 3.9458611 3.5481868 3.2173699 2.9525975 2.7385318 2.5603156 3.36189603 3.1735339 3.1245375 3.1099698 3.1071391 3.1062400 3.1061798 3.1061645 3.1061606 3.10615962 3.1061594 3.1061593 3 4.0 3 3 3 3 3.0 3.0 2.0 3 2 4.0 3 Same 2 Same 3 Same RF_1_ASE RF_2_ASE RF_3_ASE RF_4_ASE RF_5_ASE RF_6_ASE RF_7_ASE RF_8_ASE RF_9_ASE RF_10_ASE RF_11_ASE RF_12_ASE
701001906 TAAKA VODKA 80 1L 701001906 4.701657e-03 2.324110e-01 inconclusive white noise 0.25007229 0.05352414 inconclusive 65.2421581 65.6767735 65.4695085 59.6613889 55.7436966 53.1857479 51.1165171 49.5479274 47.2526994 45.3416453 42.9647688 40.5688675 8.1166667 8.1166667 8.1166667 8.1166667 8.1166667 8.1166667 8.1166667 8.1166667 8.1166667 8.1166667 8.1166667 8.1166667 85.2887355 77.6839390 73.8069104 69.2578116 64.4633563 59.9397663 57.1697840 55.5471763 53.3873148 51.7330153 49.4464658 46.9257281 14.4189452 13.2802750 13.1946172 12.3121250 11.7450798 11.4520227 10.9466142 10.6014555 10.3353892 10.0302385 9.8010743 9.6030328 85.6532674 78.3684495 78.3403061 75.3847626 70.1241569 67.8788493 64.9288995 62.8958034 60.2088286 57.8759763 55.0380537 51.8806305 14.4341932 14.2992145 14.2981344 13.8378853 13.5695530 13.3717741 13.1063023 12.8707520 12.6607333 12.4485251 12.2471629 12.0581166 74.5872838 70.6186401 66.3973333 59.6478478 53.8327383 51.5811565 48.6152222 48.0686022 47.9420718 49.6530111 50.0749767 49.5147431 16.890080 14.4266741 16.4785885 15.8949595 15.5535072 16.2036223 15.5111407 15.9504079 15.9285781 15.6921148 15.9496297 15.7800948 7.502760e+01 72.4998836 66.2607202 62.0471258 56.6378845 53.7960147 51.3101253 50.7398992 50.4118597 51.3105130 50.7607084 49.5530079 16.8900802 14.4266741 16.4785885 15.8949595 15.5535072 16.2036223 15.5111407 15.9504079 15.9285781 15.6921148 15.9496297 15.7800948 67.1468926 66.2038316 80.2528189 83.0318224 85.0611332 85.5190828 85.6981161 88.5574500 91.0191982 94.5276143 97.4637139 99.4802874 1.378831e+01 16.7230399 31.2335027 6.236520e+00 1.494705e+01 1.903011e+01 1.666967e+01 23.7685567 15.9627628 22.18950698 19.4650976 2.001956e+01 70.6317652 70.6193852 84.1328390 86.1232897 87.6434001 87.6274218 86.3545689 89.4743434 92.0583899 95.7837302 98.3255336 99.7407462 1.378831e+01 16.7230399 31.2335027 6.236520e+00 1.494705e+01 1.903011e+01 1.666967e+01 23.7685567 15.962763 22.18950698 19.465098 2.001956e+01 66.0039822 65.2669838 64.2210178 59.5624969 56.0555223 53.6185380 51.3275461 49.5178577 46.8304084 44.6489859 42.3556792 40.1835077 5.86703333 9.7629000 9.7629000 5.30776667 9.5909333 9.76290000 9.7629000 9.7629000 9.7629000 9.7629000 9.7629000 9.76290000 58.5809757 64.6758492 67.2387161 62.7200042 59.6796979 57.5146653 55.5307521 53.8214504 51.2117272 48.9734325 46.2382131 43.5778354 8.09499620 6.9148215 6.6156480 6.5633902 6.5542264 6.5526352 6.5523594 6.5523116 6.5523033 6.55230184 6.5523016 6.5523015 5 10.0 8 12 11 7 5.0 4.0 4.0 7 5 10.0 1 Same 6 Inconclusive 3 Same MLP_1_ASE MLP_2_ASE RF_3_ASE RF_4_ASE ARI_5_ASE ARI_6_ASE ARI_7_ASE ARI_8_ASE RF_9_ASE RF_10_ASE RF_11_ASE RF_12_ASE
701001907 TAAKA VODKA 80 1L 701001907 0.000000e+00 0.000000e+00 not white noise NA 0.42321723 0.01000000 not stationary 198.1483532 202.6365583 206.4005754 182.9596994 171.3135840 163.8738660 158.2928221 155.6318788 153.1012307 151.9063532 150.0285164 147.7516011 15.5316667 15.5316667 15.5316667 15.5316667 15.5316667 15.5316667 15.5316667 15.5316667 15.5316667 15.5316667 15.5316667 15.5316667 186.3383862 161.2947331 155.6102408 132.9191425 114.5520854 106.2446882 100.4079803 99.3107249 99.4926151 101.4070585 103.0827167 103.2697017 23.2996031 22.7028899 23.4093621 22.3978434 22.0325639 21.8955191 21.5314745 21.3273656 20.9641341 20.7343026 20.5200017 20.2589090 163.0706045 147.6514991 142.0327887 118.6811530 102.0842851 93.9061365 88.8143283 89.1300378 90.6734892 93.6587780 96.6549372 98.3048675 22.8958642 23.2461938 22.9222282 22.5535981 22.4030964 22.1708292 21.9334597 21.7335775 21.5290731 21.3288296 21.1394194 20.9548197 195.9989829 172.8274751 169.5288216 144.5641460 120.7028131 108.7694538 100.0483781 98.6547173 99.9286912 103.1177134 107.1926827 110.0422183 24.715734 23.8774350 25.1937409 24.4058052 24.2982615 24.6635349 24.4493511 24.6040337 24.4647506 24.4934478 24.5652805 24.4945240 1.501983e+02 143.3290122 141.7302822 119.6492689 106.8935998 97.5921329 92.7298300 94.7295674 97.4315877 102.3187664 106.9094471 111.2762217 22.9247349 23.6428572 23.5853520 23.4369136 23.5165456 23.5172404 23.4976499 23.5061535 23.5071332 23.5046404 23.5055066 23.5057268 180.1416808 162.3236925 170.7602707 164.3104602 159.7579607 155.9282852 154.1061057 157.8454601 161.2023830 167.5519152 173.5913865 178.3727557 1.762591e+01 21.0435293 50.0030273 1.000211e+00 2.200001e+01 2.500000e+01 1.900000e+01 27.0000000 19.0000000 27.00000000 25.0000000 2.400000e+01 182.8480991 165.3978276 172.7950756 165.8161092 160.9457245 156.9136823 154.9305126 158.5704392 161.8352075 168.1169377 174.1008125 178.8359459 1.700000e+01 21.0000000 50.0000000 1.000000e+00 2.200000e+01 2.500000e+01 1.900000e+01 27.0000000 19.000000 27.00000000 25.000000 2.400000e+01 156.4368270 154.9930660 152.8209379 136.5148452 124.6543834 116.2945839 111.1249615 110.0743097 110.3108224 112.0529267 113.8085748 114.6928745 17.15971000 20.2365167 20.7316200 10.18493333 20.5046500 20.73162000 19.0378000 20.7316200 19.0378000 20.7316200 20.7316200 20.73162000 135.6399232 143.3332459 139.7855526 117.0650698 97.6246387 85.2372261 80.0630062 77.6480670 77.8008573 81.3899543 87.0057808 92.5205416 17.20569305 16.8698292 23.7587437 20.3939866 21.7593247 21.6009803 24.0957281 24.4798583 25.4518303 23.91105107 24.3612270 24.3227384 28 25.0 26 23 30 22 7.0 4.0 5.0 5 8 21.0 11 Different 9 Different 3 Same MLP_1_ASE ARIMA_2_ASE MLP_3_ASE MLP_4_ASE MLP_5_ASE MLP_6_ASE MLP_7_ASE MLP_8_ASE MLP_9_ASE MLP_10_ASE MLP_11_ASE MLP_12_ASE
700005900 TAAKA VODKA 80 1L 700005900 2.343884e-02 1.671774e-01 inconclusive white noise 0.18041707 0.04977124 not stationary 1.1002137 1.2694444 1.3378205 1.4354701 1.5084188 1.5634615 1.6097375 1.6434829 1.6663105 1.6832906 1.7279526 1.7576923 1.8833333 1.8833333 1.8833333 1.8833333 1.8833333 1.8833333 1.8833333 1.8833333 1.8833333 1.8833333 1.8833333 1.8833333 1.1165974 1.3220911 1.4568656 1.5441073 1.6008962 1.6276643 1.6604292 1.6866816 1.7060960 1.7198011 1.7614605 1.7883535 2.1186626 1.9329273 1.8937849 1.8855359 1.8837975 1.8834312 1.8833539 1.8833377 1.8833342 1.8833335 1.8833334 1.8833333 1.0595516 1.3538109 1.4839001 1.5426432 1.5814597 1.6259222 1.6660457 1.6941691 1.7063527 1.7177220 1.7584874 1.7871770 2.5412846 2.2836974 1.8833333 1.8833333 1.8833333 1.8833333 1.8833333 1.8833333 1.8833333 1.8833333 1.8833333 1.8833333 1.1080114 1.1577576 1.2617732 1.3216870 1.3061257 1.3350413 1.4266053 1.5065665 1.5969981 1.6679795 1.7271516 1.7863690 3.155017 3.0403847 2.7014297 2.8771479 2.8360397 2.9954009 2.9642977 2.8963161 2.8985423 2.8660181 2.9238211 2.9203170 1.101310e+00 1.3801037 1.3854369 1.5228097 1.5577902 1.5402714 1.5416878 1.5752095 1.5914634 1.6536299 1.7103440 1.7389881 1.2338905 1.0000244 1.0000244 1.0000244 1.0000244 1.0000244 1.0000244 1.0000244 1.0000244 1.0000244 1.0000244 1.0000244 1.2181696 1.7799896 2.0477150 2.4283604 2.7262225 2.8266447 2.9445809 2.9977380 3.0762501 3.1410134 3.1891000 3.2305113 2.994324e+00 1.2209823 2.9029557 -3.791015e-01 7.401473e-01 1.855474e+00 3.035202e+00 3.0858336 3.0978952 2.04362880 3.0042736 2.972696e+00 1.1350347 1.5327785 1.7377441 2.0966865 2.4001221 2.5704244 2.7177394 2.8033499 2.8996504 2.9787477 3.0430483 3.0968104 3.179249e+00 1.6499882 3.0000000 0.000000e+00 1.000000e+00 2.000000e+00 3.000000e+00 3.0000000 3.000000 2.00000000 3.000000 3.000000e+00 1.4497370 1.6277858 1.5926255 1.7518485 1.9328607 2.0567934 2.2023114 2.2566548 2.3239697 2.3684895 2.3951467 2.4228990 2.07690000 1.2532000 2.8436333 1.09120000 1.2532000 2.07690000 2.9196333 2.9196333 2.9196333 2.0769000 2.9196333 2.91963333 1.0868414 1.2662052 1.3412578 1.4423413 1.5214453 1.5819541 1.6328541 1.6709791 1.6955640 1.7151637 1.7634119 1.7952930 1.85748712 1.8507280 1.8504071 1.8503919 1.8503912 1.8503911 1.8503911 1.8503911 1.8503911 1.85039114 1.8503911 1.8503911 3 4.0 3 4 4 3 1.0 3.0 1.0 3 4 2.0 0 Same 5 Inconclusive 0 Same ARMA_1_ASE ARI_2_ASE ARI_3_ASE ARI_4_ASE ARI_5_ASE ARI_6_ASE ARI_7_ASE ARI_8_ASE ARIMA_9_ASE ARIMA_10_ASE ARIMA_11_ASE ARIMA_12_ASE
701001768 TAAKA VODKA 80 1L 701001768 0.000000e+00 0.000000e+00 not white noise NA 0.48537100 0.10000000 inconclusive 4.8252590 4.7309000 4.6891906 4.6548744 4.4625923 4.1009000 3.8908267 3.6955154 3.6434926 3.5806949 3.4830212 3.3908573 4.7800000 4.7800000 4.7800000 4.7800000 4.7800000 4.7800000 4.7800000 4.7800000 4.7800000 4.7800000 4.7800000 4.7800000 5.7808807 5.7352446 5.5232941 5.3965745 5.0694056 4.6852788 4.3741196 4.0734054 3.9675615 3.8590111 3.7221682 3.5847486 5.6248910 5.4467598 5.2805248 5.1628121 5.0707310 5.0013829 4.9484091 4.9081590 4.8775150 4.8542023 4.8364617 4.8229630 5.2605927 5.2971241 5.2878247 5.1661669 4.8449283 4.4788421 4.1976426 3.9212539 3.8133806 3.6862767 3.5379249 3.3946633 5.2292753 5.1602537 5.1018358 5.0523925 5.0105452 4.9751268 4.9451497 4.9197779 4.8983040 4.8801291 4.8647464 4.8517269 6.4952601 6.7509692 6.8814484 6.9519907 6.6458896 6.4373570 6.0746771 5.6287433 5.4702737 5.2501518 5.0207343 4.7790625 5.007063 5.4635630 5.5001693 5.3700205 5.4207692 5.4297450 5.4130208 5.4184816 5.4201225 5.4180126 5.4185753 5.4188403 5.732139e+00 5.7316454 5.9547820 5.9448081 5.6364189 5.3917974 5.0619394 4.6936530 4.5424800 4.3541588 4.1646626 3.9649667 5.0704608 5.0704608 5.0704608 5.0704608 5.0704608 5.0704608 5.0704608 5.0704608 5.0704608 5.0704608 5.0704608 5.0704608 5.0628519 4.8568522 4.9092401 5.1366898 4.8822748 4.7841646 4.6868093 4.5409002 4.5063650 4.5045398 4.5556105 4.6106155 5.094327e+00 5.8633772 6.5140523 9.270669e+00 1.053951e+00 3.877910e+00 2.730153e+00 3.6076001 3.5055162 2.42061398 6.3499621 6.291181e+00 4.9079529 4.9796347 5.0235500 5.3625069 5.1204962 4.9727518 4.8140382 4.7272246 4.7013188 4.6820765 4.7368283 4.7764556 4.750496e+00 5.5412219 6.3569667 9.194740e+00 1.051907e+00 3.926150e+00 2.815428e+00 3.7179421 3.632111 2.55654143 6.490006 6.431425e+00 4.3015800 4.2148830 4.1777067 4.2515324 4.2137678 3.9471129 3.7287577 3.5048549 3.3129194 3.1993758 3.0721182 2.9674082 2.95280000 3.8222000 4.4437000 6.68485333 2.5756333 3.06963333 2.6436333 3.0696333 3.0696333 2.6436333 5.3402333 5.34023333 4.4760203 5.5609093 6.1915751 7.4413004 7.3220297 7.3204154 7.3389896 7.2958025 7.2740405 7.3399115 7.4404394 7.3617442 4.05054668 5.0112628 5.0765632 5.0899045 4.9679198 4.7096879 4.8428403 4.1826157 4.7815746 3.62254841 4.6861089 4.0379549 4 5.0 4 5 4 3 2.0 3.0 1.0 5 4 4.0 3 Same 3 Same 3 Same RF_1_ASE RF_2_ASE RF_3_ASE RF_4_ASE RF_5_ASE RF_6_ASE RF_7_ASE RF_8_ASE RF_9_ASE RF_10_ASE RF_11_ASE RF_12_ASE
700005850 TAAKA VODKA 80 1L 700005850 7.619964e-01 5.395173e-01 white noise white noise 0.05366716 0.10000000 inconclusive 0.7946959 0.8499524 0.8584566 0.8650806 0.8504908 0.8458498 0.8291648 0.8163306 0.8088270 0.8013113 0.7960479 0.7916831 1.6633333 1.6633333 1.6633333 1.6633333 1.6633333 1.6633333 1.6633333 1.6633333 1.6633333 1.6633333 1.6633333 1.6633333 0.8274480 0.8556140 0.8596201 0.8577027 0.8435695 0.8405124 0.8198949 0.8073862 0.8030721 0.7959836 0.7909743 0.7861360 1.3037058 1.7600904 1.6373010 1.6703373 1.6614489 1.6638403 1.6631969 1.6633700 1.6633235 1.6633360 1.6633326 1.6633335 0.9313236 0.9150902 0.8734208 0.8846560 0.8540705 0.8458284 0.8180487 0.7992410 0.8014471 0.7953921 0.7858098 0.7843329 1.1990399 1.6633333 1.6633333 1.6633333 1.6633333 1.6633333 1.6633333 1.6633333 1.6633333 1.6633333 1.6633333 1.6633333 0.7136781 0.7603013 0.7850604 0.7767056 0.7513776 0.7727133 0.7613526 0.7442265 0.7436889 0.7651053 0.7828025 0.8060640 1.627028 1.8024442 2.0871018 2.2147253 2.2693248 1.8223728 2.0396027 2.1059611 2.1475281 2.0723239 1.9786281 2.0860657 1.668124e+00 1.7099588 1.4339802 1.4716291 1.4078535 1.4279774 1.3607470 1.3316285 1.2889480 1.2815764 1.2452635 1.2593410 -0.2756279 0.6273774 0.3784424 0.4470673 0.4281492 0.4333644 0.4319267 0.4323230 0.4322138 0.4322439 0.4322356 0.4322379 2.1899248 2.3685072 2.4259557 2.4526570 2.3475776 2.3281706 2.3142204 2.2941715 2.2700343 2.2584155 2.2489090 2.2409872 1.376305e+00 1.1944979 2.9393463 1.891471e-02 1.994101e+00 3.001839e+00 1.999426e+00 2.0001789 0.9999442 2.00001740 1.9999946 3.000002e+00 2.2656312 2.5005957 2.5645920 2.5893030 2.5160865 2.4683782 2.4140848 2.3876108 2.3643841 2.3484751 2.3305555 2.3184846 1.250166e+00 1.0000000 3.0000000 0.000000e+00 2.000000e+00 3.000000e+00 2.000000e+00 2.0000000 1.000000 2.00000000 2.000000 3.000000e+00 1.5086151 1.7295398 1.8467675 1.8756080 1.8194827 1.7965394 1.7867383 1.7965108 1.7917820 1.7672508 1.7732442 1.7652827 2.07492667 1.1029667 2.5915000 0.62606667 2.0749267 2.59150000 2.0749267 2.0749267 1.1029667 2.0749267 2.0749267 2.59150000 0.7469871 0.8089189 0.8212921 0.8196412 0.8007555 0.7889079 0.7727866 0.7617197 0.7543529 0.7516042 0.7500465 0.7519794 1.67447371 1.6753555 1.6761101 1.6761764 1.6761825 1.6761831 1.6761832 1.6761832 1.6761832 1.67618318 1.6761832 1.6761832 1 3.0 2 3 3 1 1.0 2.0 1.0 1 1 2.0 1 Same 3 Same 0 Same ARI_1_ASE ARI_2_ASE ARI_3_ASE ARI_4_ASE ARI_5_ASE ARI_6_ASE ARI_7_ASE ARI_8_ASE ARI_9_ASE MLP_10_ASE MLP_11_ASE MLP_12_ASE
701001830 TAAKA VODKA 80 1L 701001830 3.036074e-07 1.098736e-05 not white noise NA 0.01094855 0.01000000 inconclusive 3.3812607 3.3274145 3.5419444 3.2107479 2.9817735 2.8650214 2.8658761 2.8812607 2.8883832 2.8969017 2.9194891 2.9395940 2.1500000 2.1500000 2.1500000 2.1500000 2.1500000 2.1500000 2.1500000 2.1500000 2.1500000 2.1500000 2.1500000 2.1500000 4.1195559 3.5713366 3.7072977 3.3318504 3.0777489 2.9445599 2.9342083 2.9409849 2.9414952 2.9446762 2.9629247 2.9794081 2.3499644 2.1716139 2.1523362 2.1502525 2.1500273 2.1500030 2.1500003 2.1500000 2.1500000 2.1500000 2.1500000 2.1500000 4.0075461 3.4573960 3.5632091 3.2119952 2.9633191 2.8283792 2.8212973 2.8343839 2.8403766 2.8490921 2.8750325 2.8932145 2.6117949 2.5657214 2.5242446 2.4869061 2.4532928 2.4230331 2.3957925 2.3712696 2.3491934 2.3293198 2.3114290 2.2953231 4.4124645 3.7578602 3.8341698 3.3643326 2.9092633 2.6517494 2.5413667 2.4553315 2.3413992 2.2748029 2.2158203 2.1626971 2.923598 3.1198527 3.2635508 3.2747402 3.1578870 3.2178726 3.2220501 3.2142954 3.2063478 3.2155823 3.2134327 3.2124481 5.693141e+00 5.0198774 5.5617559 5.3414683 5.1786422 5.1347258 5.2635862 5.2865471 5.2943238 5.2846495 5.1757291 5.0886369 1.3356365 1.5349088 1.2718390 1.1519197 1.0750150 1.0476987 1.0247556 1.0139917 1.0077459 1.0043690 1.0024185 1.0013730 4.6622079 4.5027535 4.5786104 4.2220598 4.0085668 3.8276560 3.7973333 3.7649766 3.7141669 3.6735195 3.6612415 3.6510099 4.134380e+00 2.0090290 7.0006067 4.076102e-05 3.000003e+00 3.000000e+00 2.000000e+00 3.0000000 3.0000000 2.00000000 3.0000000 4.000000e+00 4.7621704 4.6118544 4.6386722 4.2674657 4.0447418 3.8577976 3.8231672 3.7875790 3.7342582 3.6916017 3.6776798 3.6660783 4.000000e+00 2.0000000 7.0000000 0.000000e+00 3.000000e+00 3.000000e+00 2.000000e+00 3.0000000 3.000000 2.00000000 3.000000 4.000000e+00 3.8952434 3.9804560 4.0401597 3.6758753 3.3930295 3.2010656 3.1777504 3.1670737 3.1422030 3.1199983 3.1416187 3.1438423 3.50236667 1.9997667 3.5023667 0.96713333 3.0698667 3.06986667 1.9997667 3.0698667 3.0698667 1.9997667 3.0698667 3.50236667 2.7212150 2.6266601 2.6485940 2.4661611 2.2155598 2.0311468 1.8818072 1.7747177 1.6605236 1.5777955 1.5215492 1.5191932 1.96478139 2.6750292 3.3752563 2.4040338 2.6981055 2.7940376 2.7127253 2.8671529 2.0644713 2.95250704 2.6267476 1.8080634 3 4.0 5 4 3 4 5.0 3.0 2.0 3 1 3.0 0 Same 10 Different 0 Same MLP_1_ASE MLP_2_ASE MLP_3_ASE MLP_4_ASE MLP_5_ASE MLP_6_ASE MLP_7_ASE MLP_8_ASE MLP_9_ASE MLP_10_ASE MLP_11_ASE MLP_12_ASE
701001767 TAAKA VODKA 80 1L 701001767 1.572929e-01 3.914269e-01 white noise white noise 0.34274666 0.10000000 inconclusive 1.3459188 1.3023291 1.2066026 1.0946368 1.0100214 0.9544658 0.9140507 0.8667521 0.8387963 0.8400214 0.8181799 0.7995513 2.2166667 2.2166667 2.2166667 2.2166667 2.2166667 2.2166667 2.2166667 2.2166667 2.2166667 2.2166667 2.2166667 2.2166667 1.6849370 1.5191555 1.4122413 1.3255207 1.2404640 1.1440327 1.0691724 1.0128380 0.9728313 0.9649127 0.9322498 0.9059205 2.3807007 2.1586414 2.9171391 2.5688481 2.2957120 2.3980851 2.2483458 2.5293585 2.3935057 2.3247667 2.3487997 2.2723652 1.9333380 1.6235733 1.4734965 1.3692537 1.2889112 1.1850200 1.1032948 1.0376552 0.9962394 0.9859819 0.9518440 0.9239290 2.3807007 2.1586414 2.9171391 2.5688481 2.2957120 2.3980851 2.2483458 2.5293585 2.3935057 2.3247667 2.3487997 2.2723652 1.8476868 1.6458625 1.5243294 1.4577167 1.3671893 1.2673377 1.1895293 1.1448096 1.1118251 1.0889661 1.0359676 1.0036943 2.467270 2.3263118 3.1237031 2.7179263 2.4276452 2.5866173 2.4886757 2.8069577 2.6373311 2.5623943 2.6135525 2.5630514 1.750115e+00 1.6015794 1.4961143 1.4375831 1.3589958 1.2541742 1.1713232 1.1220013 1.0900889 1.0678670 1.0191809 0.9856034 2.4672700 2.3263118 3.1237031 2.7179263 2.4276452 2.5866173 2.4886757 2.8069577 2.6373311 2.5623943 2.6135525 2.5630514 2.0954669 2.3354071 2.3971244 2.3672999 2.2354135 2.1887884 2.1395257 2.0666908 2.0105044 1.9518243 1.9235242 1.9086431 1.388334e+00 -0.1222036 4.3714579 9.221621e-01 1.751937e+00 2.126097e+00 9.330889e-01 2.1345194 1.9482754 3.94710235 3.0344675 1.974070e+00 3.5248317 3.1975521 3.0058058 2.8039407 2.5891514 2.4424681 2.3937548 2.2516280 2.1680245 2.1171107 2.0662856 2.0406461 1.388334e+00 -0.1222036 4.3714579 9.221621e-01 1.751937e+00 2.126097e+00 9.330889e-01 2.1345194 1.948275 3.94710235 3.034467 1.974070e+00 2.2752853 2.2865714 2.1463304 2.0546172 1.9337087 1.8137312 1.7312740 1.6297377 1.5540143 1.4948290 1.4447854 1.4080131 1.54346667 1.4094667 3.7699333 1.54746667 2.0338667 2.03386667 1.5474667 2.0338667 2.0338667 3.8159333 2.9889667 2.03386667 1.5974004 1.5874738 1.4590806 1.3691841 1.2766082 1.2157134 1.1728828 1.1201923 1.0974608 1.0958563 1.0791525 1.0664492 2.51795322 2.5816271 2.5215890 2.5436836 2.4931962 2.5421304 2.4840087 2.5420571 2.4805325 2.54205348 2.4788255 2.5420533 1 2.0 1 2 2 2 2.0 2.0 1.0 4 2 3.0 0 Same 0 Same 0 Same EqualMeans_1_ASE EqualMeans_2_ASE EqualMeans_3_ASE EqualMeans_4_ASE EqualMeans_5_ASE EqualMeans_6_ASE EqualMeans_7_ASE EqualMeans_8_ASE EqualMeans_9_ASE EqualMeans_10_ASE EqualMeans_11_ASE EqualMeans_12_ASE
701001810 TAAKA VODKA 80 1L 701001810 0.000000e+00 0.000000e+00 not white noise NA 0.54437889 0.01060199 not stationary 2.7694231 2.9386538 3.0241239 2.5476282 2.2068590 1.9775427 1.8086172 1.6787179 1.5862322 1.5060897 1.4374883 1.3850214 2.1500000 2.1500000 2.1500000 2.1500000 2.1500000 2.1500000 2.1500000 2.1500000 2.1500000 2.1500000 2.1500000 2.1500000 3.8104860 3.4868913 3.3838308 2.9336535 2.5560414 2.3282849 2.1275674 1.9714185 1.8694536 1.8120156 1.7505586 1.6899983 2.0522846 2.0606613 2.0716803 2.0910025 2.0987020 2.1068851 2.1155365 2.1207943 2.1257431 2.1301576 2.1333904 2.1362404 4.5910109 4.3387866 4.0374311 3.4712152 3.0265545 2.7291639 2.5120868 2.3031515 2.1768817 2.0924796 1.9910859 1.8807362 1.9994117 2.0113054 2.0222596 2.0323487 2.0416410 2.0501993 2.0580817 2.0653416 2.0720280 2.0781863 2.0838583 2.0890822 4.9419848 4.5273245 4.3249139 3.8658440 3.4547432 3.1730843 2.9767132 2.7948007 2.6591141 2.6571698 2.5919980 2.5046672 2.000000 2.0000000 2.0000000 2.0000000 2.0000000 2.0000000 2.0000000 2.0000000 2.0000000 2.0000000 2.0000000 2.0000000 4.163263e+00 4.1005963 3.8469651 3.5846134 3.2781221 3.0622591 2.8507899 2.7383287 2.5955131 2.6034540 2.5522387 2.4843749 1.9763079 1.9763079 1.9763079 1.9763079 1.9763079 1.9763079 1.9763079 1.9763079 1.9763079 1.9763079 1.9763079 1.9763079 4.5007056 4.2145008 4.9602165 5.5237227 5.5113092 5.3473846 5.2607772 5.1530926 5.0493986 4.9398601 4.8464986 4.7364310 1.754320e+00 1.8136830 6.6689289 -1.672947e-01 1.869808e+00 1.862734e+00 1.907326e+00 1.9268275 0.9354361 1.95134954 1.9613037 1.967943e+00 4.2968421 4.2911908 4.8025444 5.3729971 5.2736339 5.1200821 5.0757839 4.9578981 4.8594204 4.7532709 4.6769437 4.5169437 1.511649e+00 1.5856716 6.6484741 -2.982427e-01 1.746964e+00 1.785318e+00 1.817859e+00 1.8454674 0.868891 1.88876405 1.905625 1.919930e+00 4.2627223 4.3938975 4.4888107 4.3204152 4.0250354 3.8316310 3.6507450 3.5194287 3.4388163 3.3199221 3.2178539 3.1353280 2.13353333 2.1335333 3.8364667 1.67553333 2.1335333 2.13353333 2.1335333 2.1335333 1.7475333 2.1335333 2.1335333 2.13353333 6.2323161 6.3950550 6.3344517 6.4902739 6.2317929 6.0053320 5.9584333 5.8583975 5.8103266 5.7817543 5.7268943 5.7062041 3.78075129 3.8335219 3.3440681 3.7790476 3.7876858 3.4186161 3.7704002 3.7543244 3.5564493 3.76545494 3.7096241 3.5972262 0 0.0 1 2 2 2 2.0 2.0 1.0 2 2 1.0 3 Same 4 Same 0 Same EqualMeans_1_ASE EqualMeans_2_ASE EqualMeans_3_ASE EqualMeans_4_ASE EqualMeans_5_ASE EqualMeans_6_ASE EqualMeans_7_ASE EqualMeans_8_ASE EqualMeans_9_ASE EqualMeans_10_ASE EqualMeans_11_ASE EqualMeans_12_ASE
700005866 TAAKA VODKA 80 1L 700005866 0.000000e+00 0.000000e+00 not white noise NA 0.31221025 0.03174915 not stationary 41.0203241 39.3216062 37.4481019 36.1557088 34.5091447 32.8639994 31.5960751 30.2733370 28.8379310 27.3446318 25.8320957 24.2926318 7.3283333 7.3283333 7.3283333 7.3283333 7.3283333 7.3283333 7.3283333 7.3283333 7.3283333 7.3283333 7.3283333 7.3283333 2.1423171 2.3126465 2.4994165 2.8478203 3.0488383 3.2621905 4.0197278 4.6931444 5.0472028 5.2261957 5.2745856 5.1754304 3.1421683 4.7655097 4.2451054 4.9756542 4.9146008 5.2965478 5.3803732 5.6156141 5.7338443 5.8991854 6.0148171 6.1410207 2.0775360 2.3394179 2.5571922 2.9196070 3.1780195 3.4797540 4.2895843 5.0141588 5.4157855 5.5611932 5.6039443 5.5032397 3.1421683 4.7655097 4.2451054 4.9756542 4.9146008 5.2965478 5.3803732 5.6156141 5.7338443 5.8991854 6.0148171 6.1410207 2.2144318 2.4734601 2.8964279 3.4077682 4.0111561 4.7870135 6.4359796 8.1630524 9.6417922 11.0790659 12.4832663 13.8160406 2.515230 4.0587504 3.0999274 3.6955410 3.3255503 3.5553857 3.4126137 3.5013026 3.4462097 3.4804330 3.4591738 3.4723798 2.214432e+00 2.4734601 2.8964279 3.4077682 4.0111561 4.7870135 6.4359796 8.1630524 9.6417922 11.0790659 12.4832663 13.8160406 2.5152302 4.0587504 3.0999274 3.6955410 3.3255503 3.5553857 3.4126137 3.5013026 3.4462097 3.4804330 3.4591738 3.4723798 10.2760336 10.0534371 11.9321992 14.0501086 16.4457911 18.6997705 21.5815729 24.1789929 26.3722464 28.4575525 30.5286043 32.1550920 6.541185e-01 2.0293576 3.2816330 8.918506e-01 1.890484e+00 2.598173e+00 1.513890e+00 0.4059347 1.3144753 1.25664156 1.2006290 5.160187e+00 9.2666327 8.9026054 10.6855680 13.0907783 15.4853964 17.6714293 20.6486179 23.4194441 25.6164912 27.6086889 29.5849732 31.2513160 6.541185e-01 2.0293576 3.2816330 8.918506e-01 1.890484e+00 2.598173e+00 1.513890e+00 0.4059347 1.314475 1.25664156 1.200629 5.160187e+00 22.6690955 22.3706392 21.3931192 20.2447847 19.6278890 18.8959654 19.2803284 19.4021001 19.0556658 18.7982994 18.4446686 18.0697664 0.20270000 0.2027000 0.7374667 0.20270000 0.2847000 0.73746667 0.2847000 0.2027000 0.2847000 0.2847000 0.2847000 2.72645333 11.3669222 19.5649319 18.4826638 20.4238714 19.8523646 20.4940658 19.8875187 20.0306814 19.5107474 19.2391295 18.3524754 17.5890176 6.83278071 7.6198127 9.2888563 8.2992533 8.9360892 8.7086563 8.7556370 8.4971381 8.6007666 8.56988634 8.8917538 8.8564703 4 4.0 5 4 7 7 12.0 5.0 4.0 7 6 7.0 12 Different 8 Inconclusive 5 Inconclusive ARMA_1_ASE AR_2_ASE AR_3_ASE AR_4_ASE AR_5_ASE AR_6_ASE AR_7_ASE AR_8_ASE AR_9_ASE AR_10_ASE AR_11_ASE AR_12_ASE
701001880 TAAKA VODKA 80 1L 701001880 3.857241e-01 7.674317e-01 white noise white noise 0.02966138 0.01000000 inconclusive 1.4269017 1.4461325 1.4610897 1.4794658 1.4438248 1.4059615 1.3686600 1.3381197 1.3157906 1.2974145 1.2604681 1.1828846 1.3666667 1.3666667 1.3666667 1.3666667 1.3666667 1.3666667 1.3666667 1.3666667 1.3666667 1.3666667 1.3666667 1.3666667 1.4632116 1.4606273 1.4694321 1.4854492 1.4485794 1.4099279 1.3720603 1.3410947 1.3184351 1.2997946 1.2626319 1.1848680 1.3022427 1.3553473 1.3646778 1.3663172 1.3666053 1.3666559 1.3666648 1.3666663 1.3666666 1.3666667 1.3666667 1.3666667 1.5174396 1.4948883 1.4825224 1.5006991 1.4644323 1.4215440 1.3823838 1.3492160 1.3240311 1.3028449 1.2655291 1.1871722 1.1998213 1.3666667 1.3666667 1.3666667 1.3666667 1.3666667 1.3666667 1.3666667 1.3666667 1.3666667 1.3666667 1.3666667 1.8877476 1.9194500 1.8957387 1.8800721 1.9207119 1.9062499 1.8450005 1.8043792 1.7733499 1.7299787 1.6582344 1.5742589 2.265142 2.8990216 2.4129341 2.0937681 2.4508967 2.4996365 2.3321244 2.3382486 2.4198043 2.3981070 2.3645226 2.3816840 2.006564e+00 2.3342891 2.3004118 2.3140128 2.2600330 2.2419669 2.2286639 2.2570145 2.3453982 2.3518083 2.3005831 2.2235996 2.2651424 2.8990216 2.4129341 2.0937681 2.4508967 2.4996365 2.3321244 2.3382486 2.4198043 2.3981070 2.3645226 2.3816840 2.1615656 2.1667482 1.9967441 1.9027505 1.8423261 1.8024660 1.7306281 1.6653109 1.6169190 1.5865805 1.5956469 1.5843790 7.701703e-01 1.7905603 1.0171284 2.734544e+00 1.491103e-01 1.227693e-01 1.921934e+00 0.9883702 2.0535955 2.99700475 3.9818192 1.011102e+00 3.1199556 3.1503628 2.7148049 2.6544759 2.6625206 2.6213930 2.4272105 2.3303058 2.2490123 2.1530840 2.0921738 2.0336181 6.240092e-01 1.3893508 0.4234414 1.629559e+00 -6.083827e-01 -5.406915e-01 9.984264e-01 0.1504591 1.624386 2.57950379 3.559803 8.524046e-01 1.7367648 1.7354995 1.7805959 1.7941530 1.7085816 1.6483342 1.5562342 1.4661224 1.4074715 1.3773042 1.3301063 1.2688826 1.10096667 1.1009667 1.1009667 2.47486667 0.8509667 0.85096667 2.0128667 1.1009667 2.0128667 2.4748667 2.4748667 1.10096667 1.6330388 1.6652712 1.6929307 1.7260548 1.6901861 1.6519590 1.6222425 1.5906834 1.5655486 1.5449177 1.5029218 1.4174294 1.06486765 1.0733548 1.0744504 1.0745917 1.0746099 1.0746122 1.0746125 1.0746125 1.0746126 1.07461255 1.0746126 1.0746126 2 2.0 2 2 1 1 2.0 1.0 1.0 2 1 2.0 1 Same 1 Same 0 Same EqualMeans_1_ASE EqualMeans_2_ASE EqualMeans_3_ASE EqualMeans_4_ASE EqualMeans_5_ASE EqualMeans_6_ASE EqualMeans_7_ASE EqualMeans_8_ASE EqualMeans_9_ASE EqualMeans_10_ASE EqualMeans_11_ASE EqualMeans_12_ASE
700005861 TAAKA VODKA 80 1L 700005861 2.798171e-05 8.768368e-04 not white noise NA 0.11665129 0.04796742 not stationary 3.1449053 3.4033669 3.4895207 3.0920848 2.8322387 2.6534524 2.5257478 2.4283669 2.3526261 2.2995464 2.2598471 2.2449908 1.2783333 1.2783333 1.2783333 1.2783333 1.2783333 1.2783333 1.2783333 1.2783333 1.2783333 1.2783333 1.2783333 1.2783333 3.6103811 3.7400735 3.8738059 3.5320257 3.2876049 3.0869508 2.9045681 2.7381857 2.5404546 2.4204425 2.3236917 2.2851496 2.1362137 2.1503921 1.7043704 1.5957308 1.4608462 1.4007512 1.3531158 1.3266516 1.3085121 1.2975709 1.2904464 1.2860171 2.9120469 3.2251489 3.3751316 3.1821920 2.9660736 2.8280312 2.6700627 2.5279470 2.3702667 2.2522066 2.1634190 2.1149156 1.9633104 1.8684188 1.7866728 1.7162512 1.6555854 1.6033237 1.5583020 1.5195172 1.4861054 1.4573222 1.4325264 1.4111657 3.8023323 3.7834990 3.9717565 3.8815795 3.8733549 3.7546458 3.6083021 3.4169530 3.1325053 2.8819962 2.6890521 2.5379689 2.520297 2.9617768 3.0405952 2.8864131 2.9633104 2.9523481 2.9408165 2.9505872 2.9472727 2.9470001 2.9479596 2.9474291 2.962186e+00 3.4010894 3.5663049 3.4222635 3.2474177 3.0839616 2.9365710 2.7409038 2.5170765 2.3283588 2.1689325 2.0708163 2.0995448 2.0995448 2.0995448 2.0995448 2.0995448 2.0995448 2.0995448 2.0995448 2.0995448 2.0995448 2.0995448 2.0995448 6.5209704 5.8880700 5.8051970 5.2391593 4.7597069 4.4442414 4.1696337 3.8881701 3.6435928 3.4828183 3.3458965 3.2435679 2.581237e+00 3.1689182 6.0490907 1.426667e-02 2.004146e+00 1.001205e+00 1.000350e+00 1.0001018 1.0000296 1.00000860 2.0000025 4.000001e+00 6.0699551 5.8170034 5.8041211 5.1472329 4.7108524 4.4383617 4.1424992 3.8847447 3.6384809 3.4857644 3.3418270 3.2749200 2.156258e+00 3.1286190 6.1058690 8.714302e-02 2.071729e+00 1.059042e+00 1.048599e+00 1.0400025 1.032927 1.02710284 2.022309 4.018363e+00 3.3950610 3.5112456 3.5298015 2.9141782 2.5643647 2.3416000 2.1788045 2.0736032 1.9986188 1.9341835 1.8863442 1.8537934 2.17688000 2.5442500 2.5442500 0.86166667 2.1768800 1.42700000 1.4270000 1.4270000 1.4270000 1.4270000 2.1768800 2.54425000 5.5640833 4.8671587 4.8664444 4.2422822 3.9374958 3.6749217 3.5350968 3.3913569 3.3145945 3.2298250 3.1869215 3.1501618 0.29701584 0.9926585 0.7448190 0.8818302 0.8182658 0.8484444 0.8409626 0.8516034 0.8208837 0.86068583 0.8124858 0.8635693 3 4.0 3 2 1 2 1.0 1.0 1.0 2 1 3.0 2 Same 3 Same 0 Same ARMA_1_ASE ARMA_2_ASE ARMA_3_ASE RF_4_ASE RF_5_ASE RF_6_ASE RF_7_ASE RF_8_ASE RF_9_ASE RF_10_ASE RF_11_ASE RF_12_ASE
701001850 TAAKA VODKA 80 1L 701001850 3.111778e-09 1.111885e-09 not white noise NA 0.01000000 0.01000000 inconclusive 1.6864744 1.6531410 1.6420299 1.6210897 1.6695513 1.6646795 1.6198077 1.6082692 1.5995798 1.5944231 1.5687587 1.5544231 1.7833333 1.7833333 1.7833333 1.7833333 1.7833333 1.7833333 1.7833333 1.7833333 1.7833333 1.7833333 1.7833333 1.7833333 1.2167612 1.3132914 1.3283362 1.3684879 1.4147987 1.3764311 1.3096835 1.2767104 1.2583194 1.2467150 1.2222427 1.2179406 0.9470581 1.4793827 0.9125766 1.4951652 1.3470116 1.2022296 1.5180307 1.3136316 1.4564144 1.5004856 1.4116544 1.5477606 0.9471051 0.9410728 0.9583839 0.9320713 1.0150731 1.0192416 0.9862771 0.9582185 0.9320831 0.9355995 0.9036402 0.8910035 0.6945360 1.3803241 0.8504484 1.1642663 1.0882857 1.0855645 1.1544780 1.1234983 1.1647393 1.1702968 1.1837013 1.2018058 0.6603510 0.6660583 0.6898079 0.7431496 0.7918948 0.7814434 0.7524623 0.7554578 0.7440502 0.7247367 0.6975496 0.6764127 0.751663 1.2945436 0.6991328 1.2715343 1.0815054 0.8580775 1.1862125 0.9383167 1.0657447 1.0882255 0.9535772 1.0939614 1.231704e+00 1.3687870 1.4382336 1.2802140 1.2448374 1.1547863 1.0938548 1.0693608 1.0896346 1.0644152 1.0024592 0.9485882 0.7516630 1.2945436 0.6991328 1.2715343 1.0815054 0.8580775 1.1862125 0.9383167 1.0657447 1.0882255 0.9535772 1.0939614 1.2290521 1.2306010 1.2574485 1.3136847 1.3280439 1.2604377 1.2139912 1.1989172 1.1884754 1.1820669 1.1774447 1.1588846 7.939023e-01 0.9616366 0.2798964 1.926051e+00 -3.873743e-02 1.106610e-01 9.188830e-01 0.9817491 1.0640390 -0.04758126 1.9989659 1.035383e+00 1.8266180 1.9893472 1.8271548 2.1182253 1.9236300 1.8966680 1.7713696 1.7231753 1.6788265 1.6423503 1.6187286 1.5899860 1.649683e+00 0.4027416 0.2461327 2.052215e+00 -1.627674e-01 1.252866e-01 9.607176e-01 0.9776946 1.038822 -0.02528883 2.005146 1.007060e+00 0.6625102 0.6887565 0.7526539 0.8496831 0.9215166 0.8913191 0.8472525 0.8163913 0.8152011 0.8225598 0.8185004 0.8080276 0.92503333 0.9250333 0.5430333 1.77556667 0.5430333 0.54303333 0.9250333 0.9250333 0.9250333 0.5430333 1.7755667 0.92503333 2.3060428 2.2514828 2.2333148 2.2245847 2.2964013 2.2995076 2.2461708 2.2402257 2.2354491 2.2314320 2.2038958 2.1905667 2.25170353 2.2576332 2.2580547 2.2580736 2.2580745 2.2580745 2.2580745 2.2580745 2.2580745 2.25807453 2.2580745 2.2580745 2 2.0 1 0 0 1 2.0 0.0 1.0 1 1 1.0 8 Inconclusive 13 Different 10 Different ARI_1_ASE ARI_2_ASE ARI_3_ASE ARI_4_ASE ARI_5_ASE ARI_6_ASE ARI_7_ASE ARI_8_ASE ARI_9_ASE ARI_10_ASE ARI_11_ASE ARI_12_ASE
701001901 TAAKA VODKA 80 1L 701001901 6.819545e-12 7.586510e-10 not white noise NA 0.18541887 0.01000000 not stationary 0.7879701 1.0213034 1.1033547 1.1533547 1.1454060 1.1285684 1.1388858 1.1482265 1.1731553 1.1741239 1.1772475 1.1804915 1.5333333 1.5333333 1.5333333 1.5333333 1.5333333 1.5333333 1.5333333 1.5333333 1.5333333 1.5333333 1.5333333 1.5333333 0.9039698 1.0009117 1.0833437 1.0912622 1.0673421 1.0358710 1.0316080 1.0339897 1.0580836 1.0580962 1.0645334 1.0690368 1.7174987 1.6589596 1.5938820 1.5694253 1.5521604 1.5439991 1.5390721 1.5365215 1.5350696 1.5342906 1.5338571 1.5336213 0.7687278 0.8821437 0.9522771 0.9727396 0.9590509 0.9318883 0.9316880 0.9346157 0.9576802 0.9540655 0.9598836 0.9652515 1.8236440 1.7776671 1.7389717 1.7064044 1.6789949 1.6559263 1.6365111 1.6201707 1.6064181 1.5948436 1.5851021 1.5769034 1.0773801 1.0917869 1.1141590 1.1014160 1.0167743 0.9614797 0.9095619 0.8811259 0.8776666 0.8398308 0.8324013 0.8220713 2.325581 2.1020848 2.1121215 2.0976546 2.1759317 2.1253015 2.1302943 2.1236785 2.1425054 2.1308696 2.1327198 2.1304444 7.399023e-01 0.8315413 0.8883643 0.8961124 0.8765321 0.8336705 0.8133006 0.7998427 0.8038369 0.7852240 0.7804549 0.7791951 1.9453676 1.9453676 1.9453676 1.9453676 1.9453676 1.9453676 1.9453676 1.9453676 1.9453676 1.9453676 1.9453676 1.9453676 0.6268156 0.8059307 0.8477424 0.8884257 0.9611325 0.9841951 1.0054706 1.0130132 1.0219238 1.0221565 1.0136362 1.0150753 6.237002e-01 1.8583984 0.9467154 2.979949e+00 -7.545188e-03 1.997161e+00 1.998932e+00 1.9995980 2.9998487 1.99994307 1.9999786 1.999992e+00 0.6230959 0.8141515 0.8558566 0.9235350 0.9969168 1.0146397 1.0315406 1.0370816 1.0421818 1.0407774 1.0285619 1.0280019 6.237002e-01 1.8583984 0.9467154 2.979949e+00 -7.545188e-03 1.997161e+00 1.998932e+00 1.9995980 2.999849 1.99994307 1.999979 1.999992e+00 0.4516071 0.5422331 0.6095051 0.6583964 0.6915431 0.7051798 0.7134556 0.7207142 0.7240629 0.7150633 0.7002729 0.6970824 1.22433333 2.2006667 1.2243333 2.88866667 0.9903333 2.20066667 2.2006667 2.2006667 2.8886667 2.2006667 2.2006667 2.20066667 1.4285241 1.2525328 1.2396290 1.2201557 1.2152628 1.2451508 1.2653614 1.2636243 1.2851196 1.2548559 1.2700149 1.2769984 2.66121679 1.5791660 1.4907872 1.4465495 1.4687488 1.4483961 1.4562846 1.4450147 1.4241650 1.32618285 1.4275030 1.5844270 1 4.0 2 2 2 2 3.0 2.0 3.0 2 2 1.0 4 Same 11 Different 6 Inconclusive RF_1_ASE RF_2_ASE RF_3_ASE RF_4_ASE RF_5_ASE RF_6_ASE RF_7_ASE RF_8_ASE RF_9_ASE RF_10_ASE RF_11_ASE RF_12_ASE
701001904 TAAKA VODKA 80 1L 701001904 9.048454e-08 5.283449e-07 not white noise NA 0.43473483 0.01000000 not stationary 1.1955769 1.2096795 1.2229274 1.2218590 1.2048077 1.1964316 1.1941117 1.1949359 1.1944373 1.1976282 1.2035023 1.2069017 1.4666667 1.4666667 1.4666667 1.4666667 1.4666667 1.4666667 1.4666667 1.4666667 1.4666667 1.4666667 1.4666667 1.4666667 1.2253128 1.2392695 1.2394043 1.2205312 1.2261086 1.2375913 1.2238957 1.2222534 1.2186818 1.2257325 1.2354346 1.2364830 1.7317351 2.2353856 2.6164106 1.7823203 1.8746877 2.0060020 1.6939037 1.6892508 1.7278686 1.6077762 1.5892680 1.5967780 1.4841602 1.5389074 1.4902713 1.4144033 1.3738584 1.3599818 1.3405575 1.3257438 1.3175436 1.3013227 1.3052061 1.3102041 1.5810320 2.0646698 2.6573867 1.9097428 1.9640995 1.9062874 1.9416191 1.7303295 1.7743717 1.7186676 1.6788633 1.6447738 1.1575969 1.2447261 1.3026216 1.2630766 1.3227959 1.3640579 1.3634306 1.3895943 1.3910433 1.4013556 1.4160392 1.4035249 2.194001 2.9530040 3.3859652 2.6620560 2.9488593 3.1349697 2.8452050 2.9530572 3.0325612 2.9167360 2.9570730 2.9908517 1.282673e+00 1.5206545 1.4229317 1.3809908 1.4082162 1.4251940 1.4167668 1.4330891 1.4325368 1.4267040 1.4439083 1.4253409 1.8423873 2.4863038 3.2129767 2.5352098 2.6448515 2.6991264 2.8165294 2.6127613 2.7216841 2.7222384 2.6995275 2.6989619 2.1053856 2.0948229 2.0747187 2.1651362 2.1873436 2.1930469 2.1826866 2.1993038 2.2044388 2.2261064 2.2532418 2.2204340 1.143407e+00 2.2319445 4.0112431 1.447822e-01 1.509765e+00 1.494126e+00 1.106289e+00 2.2140312 1.2356301 1.06777297 3.0917690 4.110406e+00 3.0800760 2.3915354 2.3939485 2.4090143 2.4395653 2.3694690 2.3644406 2.3630603 2.3654867 2.3960114 2.4235625 2.3890228 1.143407e+00 2.2319445 4.0112431 1.447822e-01 1.509765e+00 1.494126e+00 1.106289e+00 2.2140312 1.235630 1.06777297 3.091769 4.110406e+00 1.6903712 1.6845594 1.6856146 1.7226741 1.6956102 1.6633170 1.6492112 1.6421563 1.6287561 1.6316713 1.6350810 1.6004296 0.87646667 0.8764667 2.5648667 0.42466667 0.8764667 0.87646667 0.8764667 1.9194000 0.8764667 0.8764667 2.5808667 2.62086667 1.9014670 1.9276983 1.9066016 1.7710551 1.6984037 1.5825790 1.4851646 1.4667794 1.4124348 1.4209702 1.3300939 1.3199670 1.40707008 2.3886325 1.8354282 1.4125732 2.8722901 1.6088991 2.8731781 2.6827613 1.6022091 2.93727981 2.0625370 2.1521682 2 2.0 2 3 1 2 2.0 1.0 2.0 2 2 3.0 1 Same 1 Same 0 Same ARI_1_ASE EqualMeans_2_ASE EqualMeans_3_ASE AR_4_ASE EqualMeans_5_ASE EqualMeans_6_ASE EqualMeans_7_ASE EqualMeans_8_ASE EqualMeans_9_ASE EqualMeans_10_ASE EqualMeans_11_ASE EqualMeans_12_ASE
701000321 TAAKA VODKA 80 1L 701000321 9.021729e-04 1.759268e-02 not white noise NA 0.01899300 0.10000000 stationary 1.1710043 1.2004915 1.2094658 1.0908761 0.9925427 0.9056197 0.8398687 0.7668376 0.7063319 0.6671581 0.6332420 0.6049786 1.2166667 1.2166667 1.2166667 1.2166667 1.2166667 1.2166667 1.2166667 1.2166667 1.2166667 1.2166667 1.2166667 1.2166667 1.2294891 1.3192009 1.3555344 1.2380914 1.1219847 1.0132678 0.9271811 0.8370151 0.7745875 0.7366518 0.7016322 0.6697700 1.4136262 1.3258148 1.3652444 1.1735504 0.9831519 1.1211774 1.1476283 1.1635058 1.2537695 1.2941281 1.2613047 1.2517146 4.9505043 2.9344969 2.3457840 2.5624829 2.4150441 2.2656664 2.1414018 1.9553184 1.8213283 1.7053062 1.6001769 1.4984614 1.5723548 1.4633890 1.5054031 1.2272708 1.0921195 1.0500487 1.0002845 1.0361209 1.1136744 1.1867192 1.2578197 1.3051289 1.4342972 1.5853167 1.6797874 1.6693680 1.6072430 1.5589531 1.5251200 1.4546881 1.3651390 1.3021452 1.2429854 1.2040647 1.504535 1.4691917 1.6258440 1.5581537 1.5476994 1.5718885 1.5628395 1.5605300 1.5642155 1.5630380 1.5625864 1.5631408 1.322547e+00 1.7211078 1.8703293 1.9101641 1.8088129 1.6926424 1.6207221 1.5910010 1.5188421 1.4191297 1.3462616 1.3141439 1.2204117 1.0000166 1.0000166 1.0000166 1.0000166 1.0000166 1.0000166 1.0000166 1.0000166 1.0000166 1.0000166 1.0000166 0.6579638 0.5701615 0.7752091 0.8155160 0.8846794 0.9374149 0.9783549 0.9933732 1.0115258 1.0361741 1.0589252 1.0846531 2.000000e+00 2.0000000 4.0000000 -4.348374e-17 6.753857e-17 1.000000e+00 6.753857e-17 1.0000000 1.0000000 1.00000000 1.0000000 2.000000e+00 0.8263359 0.7231268 0.9128621 1.1243435 1.1876421 1.1582706 1.1786536 1.1696388 1.1729235 1.1849318 1.2007783 1.2167080 2.000000e+00 2.0000000 4.0000000 -2.405483e-17 -1.350771e-16 1.000000e+00 -9.344377e-17 1.0000000 1.000000 1.00000000 1.000000 2.000000e+00 0.4807360 0.5043518 0.5616449 0.5304247 0.5372993 0.5529296 0.5593234 0.5564176 0.5633958 0.5765286 0.5883527 0.6018623 1.90196667 1.9019667 2.2679667 0.41273333 0.4127333 1.04470000 0.4127333 1.0447000 1.0447000 1.0447000 1.0447000 1.90196667 3.9071392 2.5666005 2.2953243 1.9757884 1.6754489 1.4705390 1.3205687 1.1962381 1.0999955 1.0299462 0.9706569 0.9268957 2.92898406 1.1099905 0.7302893 0.4426791 1.0990789 1.0469681 1.0574663 1.0522111 1.0554095 1.07558045 1.0590376 1.0528707 2 2.0 1 1 2 2 1.0 1.0 1.0 0 1 1.0 2 Same 0 Same 3 Same RF_1_ASE RF_2_ASE RF_3_ASE RF_4_ASE RF_5_ASE RF_6_ASE RF_7_ASE RF_8_ASE RF_9_ASE RF_10_ASE RF_11_ASE RF_12_ASE
701001902 TAAKA VODKA 80 1L 701001902 0.000000e+00 1.110223e-16 not white noise NA 0.36038955 0.01000000 not stationary 1.2988034 1.3129060 1.3201709 1.4180342 1.4875214 1.5586325 1.7266422 1.8734829 1.9894017 2.0936752 2.1824864 2.2449573 1.8000000 1.8000000 1.8000000 1.8000000 1.8000000 1.8000000 1.8000000 1.8000000 1.8000000 1.8000000 1.8000000 1.8000000 1.3539749 1.3588057 1.3633975 1.3813713 1.4473666 1.5173847 1.6858683 1.8330004 1.9517698 2.0594757 2.1512192 2.2159832 3.7100420 2.9400814 2.4805010 2.2061830 2.0424458 1.9447130 1.8863775 1.8515577 1.8307742 1.8183687 1.8109641 1.8065443 1.3417939 1.3484977 1.3506908 1.3635321 1.4317118 1.5017399 1.6695923 1.8108711 1.9283069 2.0358965 2.1287877 2.1928990 3.7100420 2.9400814 2.4805010 2.2061830 2.0424458 1.9447130 1.8863775 1.8515577 1.8307742 1.8183687 1.8109641 1.8065443 1.3619844 1.3979031 1.3598847 1.1737398 1.2521387 1.3339832 1.4364247 1.4530547 1.5484084 1.6936525 1.8040564 1.8510117 3.869573 3.6125856 3.3060967 3.7829621 3.7514210 3.7702081 3.6297962 3.6826525 3.6834965 3.7152756 3.6890658 3.6921358 1.367044e+00 1.4393103 1.4454570 1.2712999 1.3515299 1.4066517 1.4658585 1.5148079 1.6072195 1.7576524 1.8606205 1.9186453 3.9779756 3.9779756 3.9779756 3.9779756 3.9779756 3.9779756 3.9779756 3.9779756 3.9779756 3.9779756 3.9779756 3.9779756 2.0390568 1.9103108 1.8639272 1.7744949 1.7821436 1.8103704 1.8886985 1.9404900 1.9854733 2.0311932 2.0698215 2.1555864 2.624291e+00 3.4435520 3.0438653 2.816562e+00 1.619171e+00 2.475240e+00 2.363029e+00 3.2778318 1.2124732 2.16253670 3.1243225 5.095097e+00 2.1767938 1.9467462 1.9045347 1.7544638 1.7551391 1.7862844 1.8603817 1.9505741 1.9893415 2.0347064 2.0739335 2.1491457 2.624291e+00 3.4435520 3.0438653 2.816562e+00 1.619171e+00 2.475240e+00 2.363029e+00 3.2778318 1.212473 2.16253670 3.124322 5.095097e+00 1.8125036 1.7418683 1.6982769 1.7598982 1.8052501 1.8507820 1.9600512 2.0390245 2.0950955 2.1456867 2.1850600 2.2469619 1.08143333 1.9650000 1.9650000 1.96500000 1.0814333 1.96500000 1.9650000 2.4627333 1.0814333 1.9650000 2.4627333 4.14833333 2.8972838 3.0439758 3.1362305 3.3683880 3.5260839 3.6875473 3.9850734 4.2524345 4.4635931 4.6311881 4.7651206 4.8565443 0.89315424 0.8257569 0.7864354 0.7645685 0.7527375 0.7464319 0.7430978 0.7413422 0.7404197 0.73993538 0.7396812 0.7395478 2 2.0 2 4 2 3 5.0 3.0 3.0 1 2 2.0 1 Same 9 Different 5 Inconclusive EqualMeans_1_ASE EqualMeans_2_ASE EqualMeans_3_ASE ARI_4_ASE ARI_5_ASE ARI_6_ASE ARI_7_ASE ARI_8_ASE ARI_9_ASE ARI_10_ASE ARI_11_ASE ARI_12_ASE
700004770 TAAKA VODKA 80 1L 700004770 0.000000e+00 0.000000e+00 not white noise NA 0.67246321 0.01000000 not stationary 2.9373276 2.9334814 2.4566438 2.3000840 2.2445583 2.2117293 2.0643972 1.9509494 1.8610028 1.8277122 1.8067681 1.7906182 3.3316667 3.3316667 3.3316667 3.3316667 3.3316667 3.3316667 3.3316667 3.3316667 3.3316667 3.3316667 3.3316667 3.3316667 3.4184434 2.5123708 2.2574863 2.3310096 2.2647927 2.1165618 2.0792477 2.1082941 2.1459321 2.2500406 2.2233113 2.2709840 2.7090858 3.0045268 2.7552078 2.9158770 2.9878752 2.9840845 3.0388172 3.0739047 3.0963842 3.1251054 3.1481911 3.1676421 2.7372199 2.7608743 2.6294740 2.5938914 2.5092408 2.5661585 2.6474384 2.7557645 2.9071031 3.0625002 3.0725270 3.1218363 2.9293446 2.9539608 2.9770709 2.9987670 3.0191356 3.0382579 3.0562102 3.0730642 3.0888869 3.1037414 3.1176871 3.1307795 4.2135756 3.1578717 2.9261509 3.1086898 3.0513504 2.9361785 3.0445157 3.2151829 3.4272852 3.6682226 3.7203684 3.8690611 2.561615 2.8651879 2.5024834 2.6232964 2.6669439 2.6019462 2.6270449 2.6327923 2.6212863 2.6263640 2.6269996 2.6249889 3.295872e+00 2.7258590 2.6967588 2.7422302 2.7448767 2.7308850 2.8594171 3.0683988 3.2781511 3.5145773 3.5802386 3.7311803 2.9725420 2.9725420 2.9725420 2.9725420 2.9725420 2.9725420 2.9725420 2.9725420 2.9725420 2.9725420 2.9725420 2.9725420 12.8951641 13.8017956 14.0855938 13.9004389 13.9267486 14.1203957 14.2350064 14.3480930 14.1482276 13.9645015 13.1432818 12.4147606 2.104223e+00 5.6896429 3.1213717 2.401091e+00 3.595388e+00 5.725325e+00 3.814024e+00 2.8738998 2.9145646 1.94209150 3.9607583 1.973405e+00 15.3958816 15.8869049 15.9214910 15.3606947 15.1356711 14.9409582 14.6203682 14.6236395 14.4563891 14.2016280 13.3333187 12.5893127 1.306533e+00 4.7272362 2.0822285 1.381773e+00 2.634530e+00 4.847809e+00 3.027774e+00 2.1796301 2.307767 1.41588971 3.507124 1.584109e+00 8.6401205 8.3117593 7.7364838 7.6932788 7.7409568 7.9931846 8.1207489 8.1529607 8.0531443 7.9974316 7.9008112 7.8253273 5.56812000 7.4269400 5.5681200 5.07279000 5.5681200 6.51265667 5.5681200 5.0727900 5.0727900 4.5102900 5.5681200 4.51029000 4.3210093 4.4547752 5.1038760 5.8181472 6.4199667 7.1546660 7.7889282 8.4227042 8.9977760 9.5352287 10.0420725 10.5573231 5.44376396 5.4995514 5.9477890 5.9171998 6.1801249 6.1055649 5.9892702 6.2901612 6.3350567 5.98461479 6.4835015 6.2549101 4 4.0 3 1 2 2 4.0 2.0 3.0 1 2 5.0 2 Same 3 Same 0 Same ARMA_1_ASE AR_2_ASE AR_3_ASE EqualMeans_4_ASE EqualMeans_5_ASE AR_6_ASE EqualMeans_7_ASE EqualMeans_8_ASE EqualMeans_9_ASE EqualMeans_10_ASE EqualMeans_11_ASE EqualMeans_12_ASE
701000320 TAAKA VODKA 80 1L 701000320 7.397740e-02 1.020833e-01 white noise white noise 0.02456406 0.10000000 stationary 0.3058120 0.2891453 0.2835897 0.2808120 0.2801709 0.2660684 0.2607570 0.2574145 0.2610826 0.2742735 0.2852991 0.2949145 1.1500000 1.1500000 1.1500000 1.1500000 1.1500000 1.1500000 1.1500000 1.1500000 1.1500000 1.1500000 1.1500000 1.1500000 0.4109945 0.3429946 0.3195829 0.3075331 0.3017865 0.2840345 0.2761569 0.2708897 0.2730606 0.2850537 0.2950993 0.3038980 1.1222686 1.1448731 1.1490522 1.1498248 1.1499676 1.1499940 1.1499989 1.1499998 1.1500000 1.1500000 1.1500000 1.1500000 0.4051081 0.3400124 0.3178584 0.3010784 0.3005917 0.2830615 0.2753256 0.2701542 0.2723935 0.2844376 0.2945231 0.3040786 1.1262931 1.1500000 1.1500000 1.1500000 1.1500000 1.1500000 1.1500000 1.1500000 1.1500000 1.1500000 1.1500000 1.1500000 0.5132315 0.4626041 0.4464509 0.4337997 0.4364314 0.4040055 0.3789017 0.3693601 0.3734112 0.3791848 0.3864571 0.3944063 1.000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 3.367507e-01 0.3334983 0.3298248 0.3271361 0.3369339 0.3258995 0.3179715 0.3165767 0.3249886 0.3380303 0.3485719 0.3592423 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.1340058 1.0679335 1.0091456 0.9661325 0.9585311 0.9523236 0.9479513 0.9351778 0.9252982 0.9250609 0.9178862 0.9119114 -2.858620e-01 0.9182829 0.9766402 9.933223e-01 -1.908896e-03 1.999454e+00 9.998440e-01 0.9999554 0.9999873 0.99999636 0.9999990 9.999997e-01 1.0951482 1.0391884 1.0373243 0.9956590 0.9750075 0.9688032 0.9617803 0.9495702 0.9384780 0.9410152 0.9327267 0.9238507 -2.835440e-01 1.0000000 1.0000000 1.000000e+00 0.000000e+00 2.000000e+00 1.000000e+00 1.0000000 1.000000 1.00000000 1.000000 1.000000e+00 0.6561855 0.6565808 0.7003539 0.7046057 0.7120659 0.7196140 0.7142612 0.6932445 0.6809154 0.6908256 0.6890456 0.6840134 0.38016667 1.0475667 1.0475667 1.05156667 0.3801667 1.79690000 1.0515667 1.0515667 1.0515667 1.0515667 1.0515667 1.05156667 1.2704633 0.7902063 0.9919788 1.7385973 1.4966013 1.2847326 1.1402432 1.0577520 1.0187777 0.9963401 0.9567935 0.9744953 0.01788975 1.0473739 0.1251189 -0.8943855 0.7900679 1.0613808 0.8380988 0.8704413 0.1268132 0.07903939 1.0291624 0.9396770 2 2.0 1 1 1 1 0.0 1.0 2.0 0 1 1.0 0 Same 0 Same 0 Same EqualMeans_1_ASE EqualMeans_2_ASE EqualMeans_3_ASE EqualMeans_4_ASE EqualMeans_5_ASE EqualMeans_6_ASE EqualMeans_7_ASE EqualMeans_8_ASE EqualMeans_9_ASE EqualMeans_10_ASE EqualMeans_11_ASE EqualMeans_12_ASE
700005926 TAAKA VODKA 80 1L 700005926 0.000000e+00 0.000000e+00 not white noise NA 0.02043425 0.01000000 inconclusive 1.2773077 1.2785897 1.2738889 1.2734615 1.2670513 1.2888462 1.3058791 1.3186538 1.3055128 1.2732051 1.2467716 1.2067949 1.5333333 1.5333333 1.5333333 1.5333333 1.5333333 1.5333333 1.5333333 1.5333333 1.5333333 1.5333333 1.5333333 1.5333333 1.5949354 1.6698877 1.5969432 1.6606368 1.5623477 1.5258236 1.4828369 1.4134233 1.3567679 1.2987954 1.2405394 1.1854457 2.0347432 1.8326340 1.7600970 1.6877429 1.6434318 1.6102652 1.5875657 1.5714169 1.5601218 1.5521628 1.5465727 1.5426409 1.4330655 1.5153141 1.4548217 1.5009097 1.3966455 1.3343924 1.2841664 1.2087831 1.1483447 1.0884805 1.0262071 0.9793421 2.2002900 2.1617869 2.1255065 2.0913205 2.0591081 2.0287553 2.0001548 1.9732053 1.9478117 1.9238840 1.9013376 1.8800928 1.4398552 1.5195100 1.5184085 1.5859954 1.5328043 1.4954347 1.4321918 1.3207035 1.2452052 1.1692806 1.1084649 1.0580159 2.033213 2.4407069 2.5035081 2.2105951 2.6555476 2.3640473 2.2586150 2.3888940 2.3980910 2.2768631 2.4599279 2.4002156 2.667315e+00 3.4118599 3.8792223 3.8945939 4.0508092 3.9659928 3.9156449 3.7875039 3.7042064 3.5755196 3.5150700 3.4031691 1.6954044 1.9238215 2.0300241 1.9299860 2.3085755 2.3687749 2.2688382 2.2545610 2.2051669 2.0706909 2.0700251 2.1066515 2.4843369 2.5933924 2.4217137 2.3937643 2.2534314 2.1727392 2.1260824 2.0622448 2.0125935 1.9728727 1.9403737 1.9068811 1.528962e+00 -0.1109384 1.9738719 -6.153660e-03 1.998551e+00 1.999659e+00 1.999920e+00 2.9999811 2.9999955 1.99999895 2.9999998 2.000000e+00 9.7833663 7.4145723 5.6429707 4.8216838 4.4154853 4.1634533 3.9056714 3.6334260 3.4048642 3.2365527 3.0866317 2.9483866 1.683491e+00 0.0158938 2.4608878 5.416634e-01 2.256431e+00 1.826491e+00 1.551416e+00 2.6000376 2.910352 2.25189453 3.394532 2.261570e+00 1.7369855 1.6840632 1.4945164 1.4199458 1.3165819 1.2587791 1.2325094 1.2087996 1.1944730 1.1628796 1.1468996 1.1314584 2.66716667 1.2049667 2.6671667 1.20496667 2.6671667 2.66716667 2.6671667 3.4851667 3.4851667 2.6671667 3.4851667 2.66716667 1.9815283 1.4925119 1.7653872 1.7753093 1.5579850 1.5285820 1.5997674 1.6019603 1.6406658 1.7676871 1.8581245 1.9469936 2.99735071 2.2192355 3.2957532 3.0317952 2.6326761 3.1494350 3.2783227 3.1141100 3.2517128 3.47956373 3.4682128 3.5185595 3 2.0 1 2 1 3 1.0 2.0 2.0 2 2 2.0 7 Inconclusive 7 Inconclusive 0 Same EqualMeans_1_ASE EqualMeans_2_ASE EqualMeans_3_ASE EqualMeans_4_ASE EqualMeans_5_ASE RF_6_ASE RF_7_ASE ARMA_8_ASE ARMA_9_ASE ARMA_10_ASE ARMA_11_ASE ARMA_12_ASE
701001800 TAAKA VODKA 80 1L 701001800 1.224362e-01 4.792812e-01 white noise white noise 0.21045181 0.03920430 not stationary 0.3269444 0.3769444 0.3799359 0.4064316 0.4248932 0.4372009 0.4547833 0.4801496 0.4956054 0.5087393 0.5194852 0.5196795 0.8333333 0.8333333 0.8333333 0.8333333 0.8333333 0.8333333 0.8333333 0.8333333 0.8333333 0.8333333 0.8333333 0.8333333 0.3326459 0.3795082 0.3816483 0.4077157 0.4259204 0.4380569 0.4555170 0.4807916 0.4961761 0.5092529 0.5199522 0.5201075 0.8399643 0.8335971 0.8333438 0.8333338 0.8333333 0.8333333 0.8333333 0.8333333 0.8333333 0.8333333 0.8333333 0.8333333 0.3269444 0.3769444 0.3799359 0.4064316 0.4248932 0.4372009 0.4547833 0.4801496 0.4956054 0.5087393 0.5194852 0.5196795 0.8333333 0.8333333 0.8333333 0.8333333 0.8333333 0.8333333 0.8333333 0.8333333 0.8333333 0.8333333 0.8333333 0.8333333 0.3038506 0.3294627 0.3613460 0.3897791 0.4590059 0.5096649 0.5446374 0.5727522 0.5942989 0.6217336 0.6417869 0.6553897 1.288629 1.1688163 1.5155480 1.1853348 1.3199271 1.2424943 1.3672014 1.2536331 1.3115650 1.2734871 1.3195815 1.2791524 3.715443e-01 0.4106859 0.4270984 0.4572844 0.4870052 0.5077215 0.5265536 0.5514860 0.5634607 0.5780082 0.5876334 0.5895793 0.8826079 0.8826079 0.8826079 0.8826079 0.8826079 0.8826079 0.8826079 0.8826079 0.8826079 0.8826079 0.8826079 0.8826079 1.3949814 1.5311940 1.5271148 1.5442603 1.5491202 1.5720521 1.5635692 1.5807947 1.6058078 1.6189796 1.6267983 1.6036859 8.789558e-01 -0.2864555 1.7378374 3.338108e-01 1.039229e+00 -1.243127e-01 1.210245e+00 0.2435835 1.0993840 0.97692315 2.0546778 1.121891e+00 1.7195772 1.7795639 1.6700771 1.6177478 1.5964515 1.5903798 1.5545462 1.5487558 1.5511204 1.5446621 1.5448047 1.5176862 8.789558e-01 -0.2864555 1.7378374 3.338108e-01 1.039229e+00 -1.243127e-01 1.210245e+00 0.2435835 1.099384 0.97692315 2.054678 1.121891e+00 0.9505822 1.1025279 1.1268384 1.2035475 1.2010364 1.2188499 1.1941809 1.2073098 1.2196685 1.2171446 1.2267873 1.2089110 0.99710000 0.1344000 0.9971000 0.13440000 1.0091000 0.13440000 1.0091000 0.1344000 1.0091000 1.0091000 1.7836667 1.00910000 0.3406550 0.4047964 0.4265396 0.4701055 0.5021653 0.5246189 0.5593738 0.5994740 0.6311114 0.6533767 0.6769308 0.6822033 0.67600436 0.6760044 0.6333375 0.6333375 0.5907647 0.5907647 0.5781798 0.5781798 0.6049114 0.60491143 0.6087298 0.6087298 1 2.0 1 2 0 1 2.0 2.0 1.0 1 1 1.0 0 Same 2 Same 0 Same ARI_1_ASE ARI_2_ASE ARI_3_ASE ARI_4_ASE EqualMeans_5_ASE EqualMeans_6_ASE EqualMeans_7_ASE EqualMeans_8_ASE EqualMeans_9_ASE EqualMeans_10_ASE EqualMeans_11_ASE EqualMeans_12_ASE
700003059 TAAKA VODKA 80 1L 700003059 0.000000e+00 0.000000e+00 not white noise NA 0.01000000 0.01000000 inconclusive 1.3594872 1.3876923 1.3475214 1.3319231 1.3246154 1.2406838 1.1990476 1.1681410 1.1401140 1.1015385 1.0662471 1.0265812 0.7333333 0.7333333 0.7333333 0.7333333 0.7333333 0.7333333 0.7333333 0.7333333 0.7333333 0.7333333 0.7333333 0.7333333 0.7845721 0.8710630 0.8805775 0.9141666 0.9391085 0.8890611 0.8853890 0.8725017 0.8647016 0.8382883 0.8151311 0.7857451 1.0481323 1.1368026 0.6405396 0.8426175 0.8769147 0.7516900 0.7846040 0.7922664 0.7587759 0.7609552 0.7608364 0.7507220 0.7822079 0.8905432 0.8879031 0.9104011 0.9222210 0.8704409 0.8534507 0.8295435 0.8112416 0.7765995 0.7437519 0.7113119 0.9216603 1.5009765 0.9665898 1.4078036 0.9958728 1.3314352 1.0134655 1.2682290 1.0223817 1.2153779 1.0249141 1.1707156 0.8020909 0.9021547 0.9007357 0.9361987 0.9587411 0.9153007 0.9283680 0.9170694 0.9204754 0.9018550 0.8799246 0.8522108 1.274858 1.3430106 0.7381308 1.0936850 1.1334287 0.9515117 1.0499681 1.0673239 1.0129014 1.0399485 1.0466752 1.0304761 2.591532e+00 2.7108124 2.4617483 2.3576535 2.2807949 2.1356822 2.1222404 2.1004201 2.0960634 2.0576792 2.0084829 1.9710193 1.2748582 1.3430106 0.7381308 1.0936850 1.1334287 0.9515117 1.0499681 1.0673239 1.0129014 1.0399485 1.0466752 1.0304761 1.7689070 1.8089697 1.7124797 1.6846435 1.7404499 1.7295824 1.7236226 1.7213262 1.6967922 1.6308052 1.5753490 1.5213369 -2.765066e-01 1.3644443 0.4884796 9.041992e-01 3.579109e+00 1.527870e+00 1.258682e+00 2.1668142 1.9137674 1.70682274 1.7917767 -9.828707e-02 1.7414562 1.8158592 1.7079300 1.6763549 1.7339938 1.7245794 1.7257332 1.7230273 1.6985303 1.6307441 1.5755449 1.5202460 -2.765066e-01 1.3644443 0.4884796 9.041992e-01 3.579109e+00 1.527870e+00 1.258682e+00 2.1668142 1.913767 1.70682274 1.791777 -9.828707e-02 1.1508434 1.1633860 1.1678729 1.1500508 1.1258950 1.0834738 1.0771968 1.0664143 1.0386723 0.9968171 0.9602420 0.9226749 0.94816667 1.4943000 0.9481667 0.94816667 1.4943000 0.94816667 0.9481667 1.4943000 1.4943000 1.4943000 1.4943000 0.10476667 0.6892937 0.7051572 0.7148292 0.7031495 0.7005994 0.6859124 0.6800124 0.6599456 0.6417744 0.6262822 0.6047723 0.6313556 0.98301281 1.3249443 1.3984097 1.1881379 1.7765832 1.4074940 1.3367883 1.5545717 1.5028699 1.55556295 1.5704580 1.6449353 1 0.0 1 1 1 1 2.0 1.0 2.0 1 2 0.0 10 Different 8 Inconclusive 2 Same MLP_1_ASE MLP_2_ASE MLP_3_ASE MLP_4_ASE MLP_5_ASE MLP_6_ASE MLP_7_ASE MLP_8_ASE MLP_9_ASE MLP_10_ASE MLP_11_ASE MLP_12_ASE
701000360 TAAKA VODKA 80 1L 701000360 0.000000e+00 0.000000e+00 not white noise NA 0.01782149 0.01000000 inconclusive 1.0547703 1.1156677 1.1445139 1.1615011 1.1998985 1.2030609 1.2641110 1.2986806 1.3393857 1.4147703 1.4755162 1.5616079 0.7083333 0.7083333 0.7083333 0.7083333 0.7083333 0.7083333 0.7083333 0.7083333 0.7083333 0.7083333 0.7083333 0.7083333 0.6719714 0.6300118 0.7577797 0.8145712 0.8591158 0.8942577 0.9422469 1.0086066 1.0556249 1.1380708 1.2053652 1.2938916 1.2880147 1.9607699 1.5563160 1.5176694 1.4476984 1.3413498 1.2904318 1.2191043 1.1667074 1.1166898 1.0722279 1.0332015 0.7409955 0.6622150 0.7679869 0.7996367 0.8200111 0.8356037 0.8565329 0.9073472 0.9353860 1.0023231 1.0571398 1.1326307 1.2880147 1.9607699 1.5563160 1.5176694 1.4476984 1.3413498 1.2904318 1.2191043 1.1667074 1.1166898 1.0722279 1.0332015 0.6897048 0.6538503 0.8242495 0.8849206 0.8868103 0.9181049 0.8907489 0.9387022 0.9217718 0.9294319 0.9334659 0.9461155 1.548404 2.2453039 2.0482803 2.0237832 2.1001411 2.0408910 2.0708135 2.0614928 2.0611865 2.0640606 2.0616581 2.0629336 6.671504e-01 0.6490383 0.7694516 0.8198088 0.8097014 0.8220716 0.8006063 0.8420725 0.8396961 0.8555306 0.8745281 0.9032365 1.5484043 2.2453039 2.0482803 2.0237832 2.1001411 2.0408910 2.0708135 2.0614928 2.0611865 2.0640606 2.0616581 2.0629336 0.8956003 0.9114742 0.9405928 0.9510732 0.9486377 0.9452439 0.9426024 0.9405613 0.9391290 0.9379581 0.9367209 0.9356515 8.040531e-01 1.5864517 0.8869675 1.774077e-01 1.950560e+00 5.516148e-02 1.980573e+00 1.0175486 0.9927707 2.00568554 0.9973925 3.001868e+00 0.8000180 0.7884722 0.8333405 0.8557746 0.8692351 0.8782087 0.8846184 0.8894258 0.8931648 0.8961560 0.8986033 0.9006428 1.280019e+00 1.6965226 1.0000000 0.000000e+00 2.000000e+00 0.000000e+00 2.000000e+00 1.0000000 1.000000 2.00000000 1.000000 3.000000e+00 0.7727211 0.7641832 0.7474693 0.7538572 0.7617306 0.7896883 0.7917159 0.8077206 0.8131983 0.8099480 0.8110756 0.8077618 1.06510000 1.0651000 1.0651000 0.31305000 1.9605333 0.31305000 1.9605333 1.0651000 1.0651000 1.9605333 1.0651000 2.01853333 1.5863008 1.2902889 2.7559933 2.9194146 2.7037700 3.5078072 3.6148993 3.6625561 4.3911635 4.6099363 4.6512789 5.3085430 2.34632999 2.0462247 3.6948482 3.1425098 2.8818331 4.0920569 3.4967159 3.5282732 4.3132387 4.15708159 4.0560629 5.0389953 1 2.0 1 1 2 1 3.0 0.0 2.0 3 2 3.0 8 Inconclusive 12 Different 13 Different ARIMA_1_ASE AR_2_ASE RF_3_ASE RF_4_ASE RF_5_ASE RF_6_ASE RF_7_ASE RF_8_ASE RF_9_ASE RF_10_ASE RF_11_ASE RF_12_ASE
700004711 TAAKA VODKA 80 1L 700004711 1.225766e-01 5.601297e-01 white noise white noise 0.34105678 0.01000000 not stationary 0.2550041 0.2575682 0.2569699 0.2547476 0.2537733 0.2535511 0.2547476 0.2746515 0.3067420 0.3466964 0.3926031 0.4436152 0.5166667 0.5166667 0.5166667 0.5166667 0.5166667 0.5166667 0.5166667 0.5166667 0.5166667 0.5166667 0.5166667 0.5166667 0.2639497 0.2614047 0.2595438 0.2566789 0.2553180 0.2548383 0.2558510 0.2756169 0.3076001 0.3474687 0.3933052 0.4442588 0.5563444 0.5136196 0.5169007 0.5166487 0.5166680 0.5166666 0.5166667 0.5166667 0.5166667 0.5166667 0.5166667 0.5166667 0.2550041 0.2575682 0.2569699 0.2547476 0.2537733 0.2535511 0.2547476 0.2746515 0.3067420 0.3466964 0.3926031 0.4436152 0.5166667 0.5166667 0.5166667 0.5166667 0.5166667 0.5166667 0.5166667 0.5166667 0.5166667 0.5166667 0.5166667 0.5166667 0.3436862 0.3307649 0.3149455 0.2949122 0.2707834 0.2572632 0.2636435 0.2862654 0.3083257 0.3313031 0.3534166 0.3804094 1.041703 0.8336566 0.8137993 0.7729034 0.7951749 0.6027690 0.8833233 0.7696072 0.7743422 0.7612159 0.7764075 0.7366452 3.361097e-01 0.3155127 0.2919478 0.2764727 0.2586763 0.2496937 0.2544425 0.2763915 0.3005871 0.3288234 0.3599117 0.3946049 0.8174024 0.6424489 0.6798952 0.6718803 0.6735958 0.6732286 0.6733072 0.6732904 0.6732940 0.6732932 0.6732934 0.6732934 0.5112069 0.4870015 0.4387405 0.4291552 0.4133043 0.4031663 0.3986917 0.3969075 0.3960754 0.3952592 0.4009168 0.4313326 5.736152e-17 1.0000000 1.0000000 5.736152e-17 1.000000e+00 7.817820e-17 1.000000e+00 1.0000000 1.0000000 1.00000000 1.0000000 1.128727e-16 0.5959641 0.5948793 0.4870828 0.4477523 0.4126828 0.4140054 0.4148010 0.4167965 0.4173774 0.4165885 0.4219115 0.4476560 5.736152e-17 1.0000000 1.0000000 5.736152e-17 1.000000e+00 7.817820e-17 1.000000e+00 1.0000000 1.000000 1.00000000 1.000000 1.128727e-16 0.3542367 0.3420991 0.3165973 0.3192477 0.3219040 0.3260338 0.3306873 0.3362587 0.3402844 0.3437473 0.3572899 0.3936388 0.05796667 0.9420667 0.9420667 0.05796667 0.9420667 0.05796667 0.9420667 0.9420667 0.9420667 0.9420667 0.9420667 0.05796667 0.2396020 0.2711712 0.2460723 0.2519696 0.2617462 0.2525414 0.2816764 0.2890390 0.3329149 0.3493588 0.3844444 0.3942741 0.49803989 0.4253242 0.7629265 0.5603698 1.1433358 0.6928211 1.3045775 0.9762882 1.6646413 1.11870466 1.8288005 1.3980319 0 1.0 1 1 1 0 0.0 2.0 2.0 2 2 2.0 0 Same 5 Inconclusive 5 Inconclusive MLP_1_ASE EqualMeans_2_ASE MLP_3_ASE MLP_4_ASE EqualMeans_5_ASE ARIMA_6_ASE ARIMA_7_ASE EqualMeans_8_ASE ARIMA_9_ASE ARIMA_10_ASE ARI_11_ASE ARI_12_ASE
aggregated_forecast = results[c("Product_Type","Product","Customer","winning_12","ACTUAL_1","ACTUAL_2","ACTUAL_3","ACTUAL_4","ACTUAL_5","ACTUAL_6","ACTUAL_7","ACTUAL_8","ACTUAL_9","ACTUAL_10","ACTUAL_11","ACTUAL_12")]
for (i in 1:z){
  if (results$winning_12[i] == "EqualMeans_12_ASE"){
    aggregated_forecast$F1[i] <- results$EqualMeans_F1[i]
    aggregated_forecast$F2[i] <- results$EqualMeans_F2[i]
    aggregated_forecast$F3[i] <- results$EqualMeans_F3[i]
    aggregated_forecast$F4[i] <- results$EqualMeans_F4[i]
    aggregated_forecast$F5[i] <- results$EqualMeans_F5[i]
    aggregated_forecast$F6[i] <- results$EqualMeans_F6[i]
    aggregated_forecast$F7[i] <- results$EqualMeans_F7[i]
    aggregated_forecast$F8[i] <- results$EqualMeans_F8[i]
    aggregated_forecast$F9[i] <- results$EqualMeans_F9[i]
    aggregated_forecast$F10[i] <- results$EqualMeans_F10[i]
    aggregated_forecast$F11[i] <- results$EqualMeans_F11[i]
    aggregated_forecast$F12[i] <- results$EqualMeans_F12[i]
  } else if (results$winning_12[i] == "AR_12_ASE"){
    aggregated_forecast$F1[i] <- results$AR_F1[i]
    aggregated_forecast$F2[i] <- results$AR_F2[i]
    aggregated_forecast$F3[i] <- results$AR_F3[i]
    aggregated_forecast$F4[i] <- results$AR_F4[i]
    aggregated_forecast$F5[i] <- results$AR_F5[i]
    aggregated_forecast$F6[i] <- results$AR_F6[i]
    aggregated_forecast$F7[i] <- results$AR_F7[i]
    aggregated_forecast$F8[i] <- results$AR_F8[i]
    aggregated_forecast$F9[i] <- results$AR_F9[i]
    aggregated_forecast$F10[i] <- results$AR_F10[i]
    aggregated_forecast$F11[i] <- results$AR_F11[i]
    aggregated_forecast$F12[i] <- results$AR_F12[i]
  } else if (results$winning_12[i] == "ARMA_12_ASE"){
    aggregated_forecast$F1[i] <- results$ARMA_F1[i]
    aggregated_forecast$F2[i] <- results$ARMA_F2[i]
    aggregated_forecast$F3[i] <- results$ARMA_F3[i]
    aggregated_forecast$F4[i] <- results$ARMA_F4[i]
    aggregated_forecast$F5[i] <- results$ARMA_F5[i]
    aggregated_forecast$F6[i] <- results$ARMA_F6[i]
    aggregated_forecast$F7[i] <- results$ARMA_F7[i]
    aggregated_forecast$F8[i] <- results$ARMA_F8[i]
    aggregated_forecast$F9[i] <- results$ARMA_F9[i]
    aggregated_forecast$F10[i] <- results$ARMA_F10[i]
    aggregated_forecast$F11[i] <- results$ARMA_F11[i]
    aggregated_forecast$F12[i] <- results$ARMA_F12[i]
  } else if (results$winning_12[i] == "ARI_12_ASE"){
    aggregated_forecast$F1[i] <- results$ARI_F1[i]
    aggregated_forecast$F2[i] <- results$ARI_F2[i]
    aggregated_forecast$F3[i] <- results$ARI_F3[i]
    aggregated_forecast$F4[i] <- results$ARI_F4[i]
    aggregated_forecast$F5[i] <- results$ARI_F5[i]
    aggregated_forecast$F6[i] <- results$ARI_F6[i]
    aggregated_forecast$F7[i] <- results$ARI_F7[i]
    aggregated_forecast$F8[i] <- results$ARI_F8[i]
    aggregated_forecast$F9[i] <- results$ARI_F9[i]
    aggregated_forecast$F10[i] <- results$ARI_F10[i]
    aggregated_forecast$F11[i] <- results$ARI_F11[i]
    aggregated_forecast$F12[i] <- results$ARI_F12[i]
  } else if (results$winning_12[i] == "ARIMA_12_ASE"){
    aggregated_forecast$F1[i] <- results$ARIMA_F1[i]
    aggregated_forecast$F2[i] <- results$ARIMA_F2[i]
    aggregated_forecast$F3[i] <- results$ARIMA_F3[i]
    aggregated_forecast$F4[i] <- results$ARIMA_F4[i]
    aggregated_forecast$F5[i] <- results$ARIMA_F5[i]
    aggregated_forecast$F6[i] <- results$ARIMA_F6[i]
    aggregated_forecast$F7[i] <- results$ARIMA_F7[i]
    aggregated_forecast$F8[i] <- results$ARIMA_F8[i]
    aggregated_forecast$F9[i] <- results$ARIMA_F9[i]
    aggregated_forecast$F10[i] <- results$ARIMA_F10[i]
    aggregated_forecast$F11[i] <- results$ARIMA_F11[i]
    aggregated_forecast$F12[i] <- results$ARIMA_F12[i]
  } else if (results$winning_12[i] == "ARI_S12_12_ASE"){
    aggregated_forecast$F1[i] <- results$ARI_S12_F1[i]
    aggregated_forecast$F2[i] <- results$ARI_S12_F2[i]
    aggregated_forecast$F3[i] <- results$ARI_S12_F3[i]
    aggregated_forecast$F4[i] <- results$ARI_S12_F4[i]
    aggregated_forecast$F5[i] <- results$ARI_S12_F5[i]
    aggregated_forecast$F6[i] <- results$ARI_S12_F6[i]
    aggregated_forecast$F7[i] <- results$ARI_S12_F7[i]
    aggregated_forecast$F8[i] <- results$ARI_S12_F8[i]
    aggregated_forecast$F9[i] <- results$ARI_S12_F9[i]
    aggregated_forecast$F10[i] <- results$ARI_S12_F10[i]
    aggregated_forecast$F11[i] <- results$ARI_S12_F11[i]
    aggregated_forecast$F12[i] <- results$ARI_S12_F12[i]
  } else if (results$winning_12[i] == "ARIMA_S12_12_ASE"){
    aggregated_forecast$F1[i] <- results$ARIMA_S12_F1[i]
    aggregated_forecast$F2[i] <- results$ARIMA_S12_F2[i]
    aggregated_forecast$F3[i] <- results$ARIMA_S12_F3[i]
    aggregated_forecast$F4[i] <- results$ARIMA_S12_F4[i]
    aggregated_forecast$F5[i] <- results$ARIMA_S12_F5[i]
    aggregated_forecast$F6[i] <- results$ARIMA_S12_F6[i]
    aggregated_forecast$F7[i] <- results$ARIMA_S12_F7[i]
    aggregated_forecast$F8[i] <- results$ARIMA_S12_F8[i]
    aggregated_forecast$F9[i] <- results$ARIMA_S12_F9[i]
    aggregated_forecast$F10[i] <- results$ARIMA_S12_F10[i]
    aggregated_forecast$F11[i] <- results$ARIMA_S12_F11[i]
    aggregated_forecast$F12[i] <- results$ARIMA_S12_F12[i]
  } else if (results$winning_12[i] == "RF_12_ASE"){
    aggregated_forecast$F1[i] <- results$RF_F1[i]
    aggregated_forecast$F2[i] <- results$RF_F2[i]
    aggregated_forecast$F3[i] <- results$RF_F3[i]
    aggregated_forecast$F4[i] <- results$RF_F4[i]
    aggregated_forecast$F5[i] <- results$RF_F5[i]
    aggregated_forecast$F6[i] <- results$RF_F6[i]
    aggregated_forecast$F7[i] <- results$RF_F7[i]
    aggregated_forecast$F8[i] <- results$RF_F8[i]
    aggregated_forecast$F9[i] <- results$RF_F9[i]
    aggregated_forecast$F10[i] <- results$RF_F10[i]
    aggregated_forecast$F11[i] <- results$RF_F11[i]
    aggregated_forecast$F12[i] <- results$RF_F12[i]
  } else if (results$winning_12[i] == "MLP_12_ASE"){
    aggregated_forecast$F1[i] <- results$MLP_F1[i]
    aggregated_forecast$F2[i] <- results$MLP_F2[i]
    aggregated_forecast$F3[i] <- results$MLP_F3[i]
    aggregated_forecast$F4[i] <- results$MLP_F4[i]
    aggregated_forecast$F5[i] <- results$MLP_F5[i]
    aggregated_forecast$F6[i] <- results$MLP_F6[i]
    aggregated_forecast$F7[i] <- results$MLP_F7[i]
    aggregated_forecast$F8[i] <- results$MLP_F8[i]
    aggregated_forecast$F9[i] <- results$MLP_F9[i]
    aggregated_forecast$F10[i] <- results$MLP_F10[i]
    aggregated_forecast$F11[i] <- results$MLP_F11[i]
    aggregated_forecast$F12[i] <- results$MLP_F12[i]
  }
}

# other time series that did not have enough data points, will use mean for forecasts
zz = nrow(combinations_mean)
results_mean <- data.frame(Product_Type=integer(),
                      Product=character(),
                      Customer=integer(),
                      EqualMeans_F1=double(),
                      EqualMeans_F2=double(),
                      EqualMeans_F3=double(),
                      EqualMeans_F4=double(),
                      EqualMeans_F5=double(),
                      EqualMeans_F6=double(),
                      EqualMeans_F7=double(),
                      EqualMeans_F8=double(),
                      EqualMeans_F9=double(),
                      EqualMeans_F10=double(),
                      EqualMeans_F11=double(),
                      EqualMeans_F12=double(),
                      ACTUAL_1=double(),
                      ACTUAL_2=double(),
                      ACTUAL_3=double(),
                      ACTUAL_4=double(),
                      ACTUAL_5=double(),
                      ACTUAL_6=double(),
                      ACTUAL_7=double(),
                      ACTUAL_8=double(),
                      ACTUAL_9=double(),
                      ACTUAL_10=double(),
                      ACTUAL_11=double(),
                      ACTUAL_12=double(),
                      stringsAsFactors = FALSE)

# loop through sample combinations
for(i in 1:zz) {
  sample_combinations1 = combinations_mean[i,]
  temp1 = inner_join(temp_mean,sample_combinations1)
  product = sample_combinations1$Product
  customer = sample_combinations1$Customer_ID
  product_type = sample_combinations1$Customer_ID
  
  results_mean[i,"Product_Type"] = product_type
  results_mean[i,"Product"] = as.character(sample_combinations1$Product)
  results_mean[i,"Customer"] = customer
  
  par(mfrow=c(1,1))
  plot.ts(temp1$STD_Cases, 
          main=c(paste("Standard Case Sales of ", product), 
                 paste("for Customer",customer)),
          xlab="Months",
          ylab="Standard Cases")
  
  j=12
  
  #Equal Means Model
  
  trainingSize = 60
  ASEHolder1 = numeric()
  ASEHolder2 = numeric()
  ASEHolder3 = numeric()
  ASEHolder4 = numeric()
  ASEHolder5 = numeric()
  ASEHolder6 = numeric()
  ASEHolder7 = numeric()
  ASEHolder8 = numeric()
  ASEHolder9 = numeric()
  ASEHolder10 = numeric()
  ASEHolder11 = numeric()
  ASEHolder12 = numeric()

  for( k in 1:(84-(trainingSize + j) + 1))
  {
    sink("file")
    model0_mean = mean(temp1$STD_Cases[k:(k+(trainingSize-1))])
    ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - model0_mean)^2)
    ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - model0_mean)^2)
    ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - model0_mean)^2)
    ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - model0_mean)^2)
    ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - model0_mean)^2)
    ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - model0_mean)^2)
    ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - model0_mean)^2)
    ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - model0_mean)^2)
    ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - model0_mean)^2)
    ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - model0_mean)^2)
    ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - model0_mean)^2)
    ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - model0_mean)^2)
    
    sink()
    
    assign(paste("EqualMeans_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - model0_mean)^2)
  }
  
  WindowedASE1 = mean(ASEHolder1)
  WindowedASE2 = mean(ASEHolder2)
  WindowedASE3 = mean(ASEHolder3)
  WindowedASE4 = mean(ASEHolder4)
  WindowedASE5 = mean(ASEHolder5)
  WindowedASE6 = mean(ASEHolder6)
  WindowedASE7 = mean(ASEHolder7)
  WindowedASE8 = mean(ASEHolder8)
  WindowedASE9 = mean(ASEHolder9)
  WindowedASE10 = mean(ASEHolder10)
  WindowedASE11 = mean(ASEHolder11)
  WindowedASE12 = mean(ASEHolder12)
  results_mean[i,paste0("EqualMeans_1_ASE")] = WindowedASE1
  results_mean[i,paste0("EqualMeans_2_ASE")] = WindowedASE2
  results_mean[i,paste0("EqualMeans_3_ASE")] = WindowedASE3
  results_mean[i,paste0("EqualMeans_4_ASE")] = WindowedASE4
  results_mean[i,paste0("EqualMeans_5_ASE")] = WindowedASE5
  results_mean[i,paste0("EqualMeans_6_ASE")] = WindowedASE6
  results_mean[i,paste0("EqualMeans_7_ASE")] = WindowedASE7
  results_mean[i,paste0("EqualMeans_8_ASE")] = WindowedASE8
  results_mean[i,paste0("EqualMeans_9_ASE")] = WindowedASE9
  results_mean[i,paste0("EqualMeans_10_ASE")] = WindowedASE10
  results_mean[i,paste0("EqualMeans_11_ASE")] = WindowedASE11
  results_mean[i,paste0("EqualMeans_12_ASE")] = WindowedASE12
  
  results_mean[i,paste0("EqualMeans_F1")] = model0_mean  
  results_mean[i,paste0("EqualMeans_F2")] = model0_mean  
  results_mean[i,paste0("EqualMeans_F3")] = model0_mean  
  results_mean[i,paste0("EqualMeans_F4")] = model0_mean  
  results_mean[i,paste0("EqualMeans_F5")] = model0_mean  
  results_mean[i,paste0("EqualMeans_F6")] = model0_mean  
  results_mean[i,paste0("EqualMeans_F7")] = model0_mean  
  results_mean[i,paste0("EqualMeans_F8")] = model0_mean  
  results_mean[i,paste0("EqualMeans_F9")] = model0_mean  
  results_mean[i,paste0("EqualMeans_F10")] = model0_mean  
  results_mean[i,paste0("EqualMeans_F11")] = model0_mean  
  results_mean[i,paste0("EqualMeans_F12")] = model0_mean  

  results_mean[i,paste0("ACTUAL_1")] = temp1$STD_Cases[73]
  results_mean[i,paste0("ACTUAL_2")] = temp1$STD_Cases[74]
  results_mean[i,paste0("ACTUAL_3")] = temp1$STD_Cases[75]
  results_mean[i,paste0("ACTUAL_4")] = temp1$STD_Cases[76]
  results_mean[i,paste0("ACTUAL_5")] = temp1$STD_Cases[77]
  results_mean[i,paste0("ACTUAL_6")] = temp1$STD_Cases[78]
  results_mean[i,paste0("ACTUAL_7")] = temp1$STD_Cases[79]
  results_mean[i,paste0("ACTUAL_8")] = temp1$STD_Cases[80]
  results_mean[i,paste0("ACTUAL_9")] = temp1$STD_Cases[81]
  results_mean[i,paste0("ACTUAL_10")] = temp1$STD_Cases[82]
  results_mean[i,paste0("ACTUAL_11")] = temp1$STD_Cases[83]
  results_mean[i,paste0("ACTUAL_12")] = temp1$STD_Cases[84]

}

Product_Type Product Customer EqualMeans_F1 EqualMeans_F2 EqualMeans_F3 EqualMeans_F4 EqualMeans_F5 EqualMeans_F6 EqualMeans_F7 EqualMeans_F8 EqualMeans_F9 EqualMeans_F10 EqualMeans_F11 EqualMeans_F12 ACTUAL_1 ACTUAL_2 ACTUAL_3 ACTUAL_4 ACTUAL_5 ACTUAL_6 ACTUAL_7 ACTUAL_8 ACTUAL_9 ACTUAL_10 ACTUAL_11 ACTUAL_12 EqualMeans_1_ASE EqualMeans_2_ASE EqualMeans_3_ASE EqualMeans_4_ASE EqualMeans_5_ASE EqualMeans_6_ASE EqualMeans_7_ASE EqualMeans_8_ASE EqualMeans_9_ASE EqualMeans_10_ASE EqualMeans_11_ASE EqualMeans_12_ASE winning_12
700005895 TAAKA VODKA 80 1L 700005895 0.4166667 0.4166667 0.4166667 0.4166667 0.4166667 0.4166667 0.4166667 0.4166667 0.4166667 0.4166667 0.4166667 0.4166667 1 2 0 2 2 0 2 2 2 2 2 2 0.4156197 0.4976709 0.5207479 0.5726709 0.6376709 0.6788675 0.7321032 0.7938248 0.8606339 0.9310043 1.0048970 1.0839957 EqualMeans_12_ASE
701000357 TAAKA VODKA 80 1L 701000357 0.6166667 0.6166667 0.6166667 0.6166667 0.6166667 0.6166667 0.6166667 0.6166667 0.6166667 0.6166667 0.6166667 0.6166667 0 0 0 0 0 0 0 0 0 0 0 0 0.3264744 0.3328846 0.3350214 0.3367308 0.3403205 0.3444231 0.3473535 0.3495513 0.3512607 0.3526282 0.3537471 0.3546795 EqualMeans_12_ASE
700005867 TAAKA VODKA 80 1L 700005867 0.2250000 0.2250000 0.2250000 0.2250000 0.2250000 0.2250000 0.2250000 0.2250000 0.2250000 0.2250000 0.2250000 0.2250000 1 1 0 0 0 0 1 0 0 0 0 1 0.2278045 0.2489583 0.2401976 0.2358173 0.2237019 0.2160524 0.2173649 0.2183494 0.2135595 0.2099840 0.2072917 0.2090011 EqualMeans_12_ASE
701001908 TAAKA VODKA 80 1L 701001908 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0 0 0 0 0 0 0 0 0 0 0 0 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 EqualMeans_12_ASE

Forecast by Product (Aggregated)


results <- data.frame(Product_Type=integer(),
                      Product=character(),
                      Customer=integer(),
                      ljung_10=double(),
                      ljung_24=double(),
                      ljung_results=character(),
                      top_5_bic=character(),
                      ADF=double(),
                      KPSS=double(),
                      stationarity_results=character(),
                      EqualMeans_1_ASE=double(),
                      EqualMeans_2_ASE=double(),
                      EqualMeans_3_ASE=double(),
                      EqualMeans_4_ASE=double(),
                      EqualMeans_5_ASE=double(),
                      EqualMeans_6_ASE=double(),
                      EqualMeans_7_ASE=double(),
                      EqualMeans_8_ASE=double(),
                      EqualMeans_9_ASE=double(),
                      EqualMeans_10_ASE=double(),
                      EqualMeans_11_ASE=double(),
                      EqualMeans_12_ASE=double(),
                      EqualMeans_F1=double(),
                      EqualMeans_F2=double(),
                      EqualMeans_F3=double(),
                      EqualMeans_F4=double(),
                      EqualMeans_F5=double(),
                      EqualMeans_F6=double(),
                      EqualMeans_F7=double(),
                      EqualMeans_F8=double(),
                      EqualMeans_F9=double(),
                      EqualMeans_F10=double(),
                      EqualMeans_F11=double(),
                      EqualMeans_F12=double(),
                      AR_1_ASE=double(),
                      AR_2_ASE=double(),
                      AR_3_ASE=double(),
                      AR_4_ASE=double(),
                      AR_5_ASE=double(),
                      AR_6_ASE=double(),
                      AR_7_ASE=double(),
                      AR_8_ASE=double(),
                      AR_9_ASE=double(),
                      AR_10_ASE=double(),
                      AR_11_ASE=double(),
                      AR_12_ASE=double(),
                      AR_F1=double(),
                      AR_F2=double(),
                      AR_F3=double(),
                      AR_F4=double(),
                      AR_F5=double(),
                      AR_F6=double(),
                      AR_F7=double(),
                      AR_F8=double(),
                      AR_F9=double(),
                      AR_F10=double(),
                      AR_F11=double(),
                      AR_F12=double(),
                      ARMA_1_ASE=double(),
                      ARMA_2_ASE=double(),
                      ARMA_3_ASE=double(),
                      ARMA_4_ASE=double(),
                      ARMA_5_ASE=double(),
                      ARMA_6_ASE=double(),
                      ARMA_7_ASE=double(),
                      ARMA_8_ASE=double(),
                      ARMA_9_ASE=double(),
                      ARMA_10_ASE=double(),
                      ARMA_11_ASE=double(),
                      ARMA_12_ASE=double(),
                      ARMA_F1=double(),
                      ARMA_F2=double(),
                      ARMA_F3=double(),
                      ARMA_F4=double(),
                      ARMA_F5=double(),
                      ARMA_F6=double(),
                      ARMA_F7=double(),
                      ARMA_F8=double(),
                      ARMA_F9=double(),
                      ARMA_F10=double(),
                      ARMA_F11=double(),
                      ARMA_F12=double(),
                      ARI_1_ASE=double(),
                      ARI_2_ASE=double(),
                      ARI_3_ASE=double(),
                      ARI_4_ASE=double(),
                      ARI_5_ASE=double(),
                      ARI_6_ASE=double(),
                      ARI_7_ASE=double(),
                      ARI_8_ASE=double(),
                      ARI_9_ASE=double(),
                      ARI_10_ASE=double(),
                      ARI_11_ASE=double(),
                      ARI_12_ASE=double(),
                      ARI_F1=double(),
                      ARI_F2=double(),
                      ARI_F3=double(),
                      ARI_F4=double(),
                      ARI_F5=double(),
                      ARI_F6=double(),
                      ARI_F7=double(),
                      ARI_F8=double(),
                      ARI_F9=double(),
                      ARI_F10=double(),
                      ARI_F11=double(),
                      ARI_F12=double(),
                      ARIMA_1_ASE=double(),
                      ARIMA_2_ASE=double(),
                      ARIMA_3_ASE=double(),
                      ARIMA_4_ASE=double(),
                      ARIMA_5_ASE=double(),
                      ARIMA_6_ASE=double(),
                      ARIMA_7_ASE=double(),
                      ARIMA_8_ASE=double(),
                      ARIMA_9_ASE=double(),
                      ARIMA_10_ASE=double(),
                      ARIMA_11_ASE=double(),
                      ARIMA_12_ASE=double(),
                      ARIMA_F1=double(),
                      ARIMA_F2=double(),
                      ARIMA_F3=double(),
                      ARIMA_F4=double(),
                      ARIMA_F5=double(),
                      ARIMA_F6=double(),
                      ARIMA_F7=double(),
                      ARIMA_F8=double(),
                      ARIMA_F9=double(),
                      ARIMA_F10=double(),
                      ARIMA_F11=double(),
                      ARIMA_F12=double(),
                      ARI_S12_1_ASE=double(),
                      ARI_S12_2_ASE=double(),
                      ARI_S12_3_ASE=double(),
                      ARI_S12_4_ASE=double(),
                      ARI_S12_5_ASE=double(),
                      ARI_S12_6_ASE=double(),
                      ARI_S12_7_ASE=double(),
                      ARI_S12_8_ASE=double(),
                      ARI_S12_9_ASE=double(),
                      ARI_S12_10_ASE=double(),
                      ARI_S12_11_ASE=double(),
                      ARI_S12_12_ASE=double(),
                      ARI_S12_F1=double(),
                      ARI_S12_F2=double(),
                      ARI_S12_F3=double(),
                      ARI_S12_F4=double(),
                      ARI_S12_F5=double(),
                      ARI_S12_F6=double(),
                      ARI_S12_F7=double(),
                      ARI_S12_F8=double(),
                      ARI_S12_F9=double(),
                      ARI_S12_F10=double(),
                      ARI_S12_F11=double(),
                      ARI_S12_F12=double(),
                      ARIMA_S12_1_ASE=double(),
                      ARIMA_S12_2_ASE=double(),
                      ARIMA_S12_3_ASE=double(),
                      ARIMA_S12_4_ASE=double(),
                      ARIMA_S12_5_ASE=double(),
                      ARIMA_S12_6_ASE=double(),
                      ARIMA_S12_7_ASE=double(),
                      ARIMA_S12_8_ASE=double(),
                      ARIMA_S12_9_ASE=double(),
                      ARIMA_S12_10_ASE=double(),
                      ARIMA_S12_11_ASE=double(),
                      ARIMA_S12_12_ASE=double(),
                      ARIMA_S12_F1=double(),
                      ARIMA_S12_F2=double(),
                      ARIMA_S12_F3=double(),
                      ARIMA_S12_F4=double(),
                      ARIMA_S12_F5=double(),
                      ARIMA_S12_F6=double(),
                      ARIMA_S12_F7=double(),
                      ARIMA_S12_F8=double(),
                      ARIMA_S12_F9=double(),
                      ARIMA_S12_F10=double(),
                      ARIMA_S12_F11=double(),
                      ARIMA_S12_F12=double(),
                      RF_1_ASE=double(),
                      RF_2_ASE=double(),
                      RF_3_ASE=double(),
                      RF_4_ASE=double(),
                      RF_5_ASE=double(),
                      RF_6_ASE=double(),
                      RF_7_ASE=double(),
                      RF_8_ASE=double(),
                      RF_9_ASE=double(),
                      RF_10_ASE=double(),
                      RF_11_ASE=double(),
                      RF_12_ASE=double(),
                      RF_F1=double(),
                      RF_F2=double(),
                      RF_F3=double(),
                      RF_F4=double(),
                      RF_F5=double(),
                      RF_F6=double(),
                      RF_F7=double(),
                      RF_F8=double(),
                      RF_F9=double(),
                      RF_F10=double(),
                      RF_F11=double(),
                      RF_F12=double(),
                      MLP_1_ASE=double(),
                      MLP_2_ASE=double(),
                      MLP_3_ASE=double(),
                      MLP_4_ASE=double(),
                      MLP_5_ASE=double(),
                      MLP_6_ASE=double(),
                      MLP_7_ASE=double(),
                      MLP_8_ASE=double(),
                      MLP_9_ASE=double(),
                      MLP_10_ASE=double(),
                      MLP_11_ASE=double(),
                      MLP_12_ASE=double(),
                      MLP_F1=double(),
                      MLP_F2=double(),
                      MLP_F3=double(),
                      MLP_F4=double(),
                      MLP_F5=double(),
                      MLP_F6=double(),
                      MLP_F7=double(),
                      MLP_F8=double(),
                      MLP_F9=double(),
                      MLP_F10=double(),
                      MLP_F11=double(),
                      MLP_F12=double(),
                      ACTUAL_1=double(),
                      ACTUAL_2=double(),
                      ACTUAL_3=double(),
                      ACTUAL_4=double(),
                      ACTUAL_5=double(),
                      ACTUAL_6=double(),
                      ACTUAL_7=double(),
                      ACTUAL_8=double(),
                      ACTUAL_9=double(),
                      ACTUAL_10=double(),
                      ACTUAL_11=double(),
                      ACTUAL_12=double(),
                      AR_F_Tally=double(),
                      AR_F_Conclusion=double(),
                      ARI_F_Tally=double(),
                      ARI_F_Conclusion=double(),
                      ARIS_F_Tally=double(),
                      ARIS_F_Conclusion=double(),
                      stringsAsFactors = FALSE)

# loop through sample combinations
  i=1
  temp1 = df_taaka_summarized

  par(mfrow=c(1,1))
  plot.ts(temp1$STD_Cases, 
          main="TAAKA VODKA 80  1L",
          xlab="Months",
          ylab="Standard Cases")

Obs 0.581064 0.2907099 0.09796717 -0.002900433 0.1054023 0.1422157 0.06115488 0.0360746 -0.1158591 -0.1599279 
The Ljung-Box test with K=10 has a p-value of 2.322229e-06 .
Obs 0.581064 0.2907099 0.09796717 -0.002900433 0.1054023 0.1422157 0.06115488 0.0360746 -0.1158591 -0.1599279 -0.1164521 -0.0414574 0.03658722 0.1325334 0.08610644 -0.1175143 -0.1852131 -0.1792189 -0.07936305 0.08417133 0.0944759 0.02650935 -0.07443002 -0.1870262 
The Ljung-Box test with K=24 has a p-value of 1.124084e-05 .
[1] "Ljung-Box test results: At a significance level of 0.05, we reject the null hypothesis that this dataset is white noise."
---------WORKING... PLEASE WAIT... 


Five Smallest Values of  bic 
[1] "Both tests for stationarity were inconclusive."
  j=12
  
  #Equal Means Model
  
  trainingSize = 60
  ASEHolder1 = numeric()
  ASEHolder2 = numeric()
  ASEHolder3 = numeric()
  ASEHolder4 = numeric()
  ASEHolder5 = numeric()
  ASEHolder6 = numeric()
  ASEHolder7 = numeric()
  ASEHolder8 = numeric()
  ASEHolder9 = numeric()
  ASEHolder10 = numeric()
  ASEHolder11 = numeric()
  ASEHolder12 = numeric()

  for( k in 1:(84-(trainingSize + j) + 1))
  {
    sink("file")
    model0_mean = mean(temp1$STD_Cases[k:(k+(trainingSize-1))])
    ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - model0_mean)^2)
    ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - model0_mean)^2)
    ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - model0_mean)^2)
    ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - model0_mean)^2)
    ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - model0_mean)^2)
    ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - model0_mean)^2)
    ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - model0_mean)^2)
    ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - model0_mean)^2)
    ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - model0_mean)^2)
    ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - model0_mean)^2)
    ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - model0_mean)^2)
    ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - model0_mean)^2)
    sink()
    
    assign(paste("EqualMeans_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - model0_mean)^2)
    assign(paste("EqualMeans_DF_",k,sep=""),trainingSize-1)
  }
  
  WindowedASE1 = mean(ASEHolder1)
  WindowedASE2 = mean(ASEHolder2)
  WindowedASE3 = mean(ASEHolder3)
  WindowedASE4 = mean(ASEHolder4)
  WindowedASE5 = mean(ASEHolder5)
  WindowedASE6 = mean(ASEHolder6)
  WindowedASE7 = mean(ASEHolder7)
  WindowedASE8 = mean(ASEHolder8)
  WindowedASE9 = mean(ASEHolder9)
  WindowedASE10 = mean(ASEHolder10)
  WindowedASE11 = mean(ASEHolder11)
  WindowedASE12 = mean(ASEHolder12)
  results[i,paste0("EqualMeans_1_ASE")] = WindowedASE1
  results[i,paste0("EqualMeans_2_ASE")] = WindowedASE2
  results[i,paste0("EqualMeans_3_ASE")] = WindowedASE3
  results[i,paste0("EqualMeans_4_ASE")] = WindowedASE4
  results[i,paste0("EqualMeans_5_ASE")] = WindowedASE5
  results[i,paste0("EqualMeans_6_ASE")] = WindowedASE6
  results[i,paste0("EqualMeans_7_ASE")] = WindowedASE7
  results[i,paste0("EqualMeans_8_ASE")] = WindowedASE8
  results[i,paste0("EqualMeans_9_ASE")] = WindowedASE9
  results[i,paste0("EqualMeans_10_ASE")] = WindowedASE10
  results[i,paste0("EqualMeans_11_ASE")] = WindowedASE11
  results[i,paste0("EqualMeans_12_ASE")] = WindowedASE12
  results[i,paste0("EqualMeans_F1")] = model0_mean  
  results[i,paste0("EqualMeans_F2")] = model0_mean  
  results[i,paste0("EqualMeans_F3")] = model0_mean  
  results[i,paste0("EqualMeans_F4")] = model0_mean  
  results[i,paste0("EqualMeans_F5")] = model0_mean  
  results[i,paste0("EqualMeans_F6")] = model0_mean  
  results[i,paste0("EqualMeans_F7")] = model0_mean  
  results[i,paste0("EqualMeans_F8")] = model0_mean  
  results[i,paste0("EqualMeans_F9")] = model0_mean  
  results[i,paste0("EqualMeans_F10")] = model0_mean  
  results[i,paste0("EqualMeans_F11")] = model0_mean  
  results[i,paste0("EqualMeans_F12")] = model0_mean  

  #AR Model
  
  trainingSize = 60
  ASEHolder1 = numeric()
  ASEHolder2 = numeric()
  ASEHolder3 = numeric()
  ASEHolder4 = numeric()
  ASEHolder5 = numeric()
  ASEHolder6 = numeric()
  ASEHolder7 = numeric()
  ASEHolder8 = numeric()
  ASEHolder9 = numeric()
  ASEHolder10 = numeric()
  ASEHolder11 = numeric()
  ASEHolder12 = numeric()
  
  for( k in 1:(84-(trainingSize + j) + 1))
  {
    sink("file")
    model1 = invisible(aic.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],q=0,type="aic"))
    model1 = invisible(aic.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],q=0,type="aic"))
    if (model1$p == 0){
      newphi = 1
    } else {
      newphi = model1$p
    } 
    model1_est = invisible(est.ar.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],p=newphi))
    forecasts = fore.aruma.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],phi = model1_est$phi, theta = 0, s = 0, d = 0,n.ahead = j,plot=FALSE)

    ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - forecasts$f[1:1])^2)
    ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - forecasts$f[1:2])^2)
    ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - forecasts$f[1:3])^2)
    ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - forecasts$f[1:4])^2)
    ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - forecasts$f[1:5])^2)
    ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - forecasts$f[1:6])^2)
    ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - forecasts$f[1:7])^2)
    ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - forecasts$f[1:8])^2)
    ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - forecasts$f[1:9])^2)
    ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - forecasts$f[1:10])^2)
    ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - forecasts$f[1:11])^2)
    ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - forecasts$f[1:12])^2)
    sink()
    
    assign(paste("AR_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - forecasts$f)^2)
    assign(paste("AR_DF_",k,sep=""),trainingSize-(newphi+1))

  }
  
  WindowedASE1 = mean(ASEHolder1)
  WindowedASE2 = mean(ASEHolder2)
  WindowedASE3 = mean(ASEHolder3)
  WindowedASE4 = mean(ASEHolder4)
  WindowedASE5 = mean(ASEHolder5)
  WindowedASE6 = mean(ASEHolder6)
  WindowedASE7 = mean(ASEHolder7)
  WindowedASE8 = mean(ASEHolder8)
  WindowedASE9 = mean(ASEHolder9)
  WindowedASE10 = mean(ASEHolder10)
  WindowedASE11 = mean(ASEHolder11)
  WindowedASE12 = mean(ASEHolder12)
  results[i,paste0("AR_1_ASE")] = WindowedASE1
  results[i,paste0("AR_2_ASE")] = WindowedASE2
  results[i,paste0("AR_3_ASE")] = WindowedASE3
  results[i,paste0("AR_4_ASE")] = WindowedASE4
  results[i,paste0("AR_5_ASE")] = WindowedASE5
  results[i,paste0("AR_6_ASE")] = WindowedASE6
  results[i,paste0("AR_7_ASE")] = WindowedASE7
  results[i,paste0("AR_8_ASE")] = WindowedASE8
  results[i,paste0("AR_9_ASE")] = WindowedASE9
  results[i,paste0("AR_10_ASE")] = WindowedASE10
  results[i,paste0("AR_11_ASE")] = WindowedASE11
  results[i,paste0("AR_12_ASE")] = WindowedASE12
  results[i,paste0("AR_F1")] = forecasts$f[1]  
  results[i,paste0("AR_F2")] = forecasts$f[2]   
  results[i,paste0("AR_F3")] = forecasts$f[3]   
  results[i,paste0("AR_F4")] = forecasts$f[4]   
  results[i,paste0("AR_F5")] = forecasts$f[5]   
  results[i,paste0("AR_F6")] = forecasts$f[6]   
  results[i,paste0("AR_F7")] = forecasts$f[7]   
  results[i,paste0("AR_F8")] = forecasts$f[8]   
  results[i,paste0("AR_F9")] = forecasts$f[9]   
  results[i,paste0("AR_F10")] = forecasts$f[10]   
  results[i,paste0("AR_F11")] = forecasts$f[11]   
  results[i,paste0("AR_F12")] = forecasts$f[12]  

  
  #ARMA Model
  
  trainingSize = 60
  ASEHolder1 = numeric()
  ASEHolder2 = numeric()
  ASEHolder3 = numeric()
  ASEHolder4 = numeric()
  ASEHolder5 = numeric()
  ASEHolder6 = numeric()
  ASEHolder7 = numeric()
  ASEHolder8 = numeric()
  ASEHolder9 = numeric()
  ASEHolder10 = numeric()
  ASEHolder11 = numeric()
  ASEHolder12 = numeric()
  
  for( k in 1:(84-(trainingSize + j) + 1))
  {
    sink("file")
    model1 = invisible(aic.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],type="aic"))
    model1_est = invisible(est.arma.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],p=model1$p,q=model1$q))
    forecasts = fore.aruma.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],phi = model1_est$phi, theta = model1_est$theta, s = 0, d = 0,n.ahead = j,plot=FALSE)

    ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - forecasts$f[1:1])^2)
    ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - forecasts$f[1:2])^2)
    ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - forecasts$f[1:3])^2)
    ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - forecasts$f[1:4])^2)
    ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - forecasts$f[1:5])^2)
    ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - forecasts$f[1:6])^2)
    ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - forecasts$f[1:7])^2)
    ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - forecasts$f[1:8])^2)
    ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - forecasts$f[1:9])^2)
    ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - forecasts$f[1:10])^2)
    ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - forecasts$f[1:11])^2)
    ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - forecasts$f[1:12])^2)
    sink()
    
    assign(paste("ARMA_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - forecasts$f)^2)

  }
  
  WindowedASE1 = mean(ASEHolder1)
  WindowedASE2 = mean(ASEHolder2)
  WindowedASE3 = mean(ASEHolder3)
  WindowedASE4 = mean(ASEHolder4)
  WindowedASE5 = mean(ASEHolder5)
  WindowedASE6 = mean(ASEHolder6)
  WindowedASE7 = mean(ASEHolder7)
  WindowedASE8 = mean(ASEHolder8)
  WindowedASE9 = mean(ASEHolder9)
  WindowedASE10 = mean(ASEHolder10)
  WindowedASE11 = mean(ASEHolder11)
  WindowedASE12 = mean(ASEHolder12)
  results[i,paste0("ARMA_1_ASE")] = WindowedASE1
  results[i,paste0("ARMA_2_ASE")] = WindowedASE2
  results[i,paste0("ARMA_3_ASE")] = WindowedASE3
  results[i,paste0("ARMA_4_ASE")] = WindowedASE4
  results[i,paste0("ARMA_5_ASE")] = WindowedASE5
  results[i,paste0("ARMA_6_ASE")] = WindowedASE6
  results[i,paste0("ARMA_7_ASE")] = WindowedASE7
  results[i,paste0("ARMA_8_ASE")] = WindowedASE8
  results[i,paste0("ARMA_9_ASE")] = WindowedASE9
  results[i,paste0("ARMA_10_ASE")] = WindowedASE10
  results[i,paste0("ARMA_11_ASE")] = WindowedASE11
  results[i,paste0("ARMA_12_ASE")] = WindowedASE12
  results[i,paste0("ARMA_F1")] = forecasts$f[1]  
  results[i,paste0("ARMA_F2")] = forecasts$f[2]   
  results[i,paste0("ARMA_F3")] = forecasts$f[3]   
  results[i,paste0("ARMA_F4")] = forecasts$f[4]   
  results[i,paste0("ARMA_F5")] = forecasts$f[5]   
  results[i,paste0("ARMA_F6")] = forecasts$f[6]   
  results[i,paste0("ARMA_F7")] = forecasts$f[7]   
  results[i,paste0("ARMA_F8")] = forecasts$f[8]   
  results[i,paste0("ARMA_F9")] = forecasts$f[9]   
  results[i,paste0("ARMA_F10")] = forecasts$f[10]   
  results[i,paste0("ARMA_F11")] = forecasts$f[11]   
  results[i,paste0("ARMA_F12")] = forecasts$f[12]  

  
  
  #ARIMA Model with q=0 and d=1
  nulldev()
  temp2 = artrans.wge(temp1$STD_Cases,1)
  dev.off()
png 
  2 
  trainingSize = 60
  ASEHolder1 = numeric()
  ASEHolder2 = numeric()
  ASEHolder3 = numeric()
  ASEHolder4 = numeric()
  ASEHolder5 = numeric()
  ASEHolder6 = numeric()
  ASEHolder7 = numeric()
  ASEHolder8 = numeric()
  ASEHolder9 = numeric()
  ASEHolder10 = numeric()
  ASEHolder11 = numeric()
  ASEHolder12 = numeric()
    
  for( k in 1:(84-(trainingSize + j) + 1))
  {
    sink("file")
    model1 = invisible(aic.wge(temp2[k:(k+(trainingSize-1-1))],q=0,type="aic"))
    model1_est = invisible(est.ar.wge(temp2[k:(k+(trainingSize-1-1))],p=model1$p))
    forecasts = fore.aruma.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],phi = model1_est$phi, theta = 0, s = 0, d = 1,n.ahead = j,plot=FALSE)
    ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - forecasts$f[1:1])^2)
    ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - forecasts$f[1:2])^2)
    ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - forecasts$f[1:3])^2)
    ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - forecasts$f[1:4])^2)
    ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - forecasts$f[1:5])^2)
    ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - forecasts$f[1:6])^2)
    ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - forecasts$f[1:7])^2)
    ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - forecasts$f[1:8])^2)
    ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - forecasts$f[1:9])^2)
    ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - forecasts$f[1:10])^2)
    ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - forecasts$f[1:11])^2)
    ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - forecasts$f[1:12])^2)
    sink()
    
    assign(paste("ARI_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - forecasts$f)^2)
    assign(paste("ARI_DF_",k,sep=""),trainingSize-(model1$p+1))

  }
  
  WindowedASE1 = mean(ASEHolder1)
  WindowedASE2 = mean(ASEHolder2)
  WindowedASE3 = mean(ASEHolder3)
  WindowedASE4 = mean(ASEHolder4)
  WindowedASE5 = mean(ASEHolder5)
  WindowedASE6 = mean(ASEHolder6)
  WindowedASE7 = mean(ASEHolder7)
  WindowedASE8 = mean(ASEHolder8)
  WindowedASE9 = mean(ASEHolder9)
  WindowedASE10 = mean(ASEHolder10)
  WindowedASE11 = mean(ASEHolder11)
  WindowedASE12 = mean(ASEHolder12)
  results[i,paste0("ARI_1_ASE")] = WindowedASE1
  results[i,paste0("ARI_2_ASE")] = WindowedASE2
  results[i,paste0("ARI_3_ASE")] = WindowedASE3
  results[i,paste0("ARI_4_ASE")] = WindowedASE4
  results[i,paste0("ARI_5_ASE")] = WindowedASE5
  results[i,paste0("ARI_6_ASE")] = WindowedASE6
  results[i,paste0("ARI_7_ASE")] = WindowedASE7
  results[i,paste0("ARI_8_ASE")] = WindowedASE8
  results[i,paste0("ARI_9_ASE")] = WindowedASE9
  results[i,paste0("ARI_10_ASE")] = WindowedASE10
  results[i,paste0("ARI_11_ASE")] = WindowedASE11
  results[i,paste0("ARI_12_ASE")] = WindowedASE12
  results[i,paste0("ARI_F1")] = forecasts$f[1]  
  results[i,paste0("ARI_F2")] = forecasts$f[2]   
  results[i,paste0("ARI_F3")] = forecasts$f[3]   
  results[i,paste0("ARI_F4")] = forecasts$f[4]   
  results[i,paste0("ARI_F5")] = forecasts$f[5]   
  results[i,paste0("ARI_F6")] = forecasts$f[6]   
  results[i,paste0("ARI_F7")] = forecasts$f[7]   
  results[i,paste0("ARI_F8")] = forecasts$f[8]   
  results[i,paste0("ARI_F9")] = forecasts$f[9]   
  results[i,paste0("ARI_F10")] = forecasts$f[10]   
  results[i,paste0("ARI_F11")] = forecasts$f[11]   
  results[i,paste0("ARI_F12")] = forecasts$f[12]

  
  #ARIMA Model with d=1
  nulldev()
  temp2 = artrans.wge(temp1$STD_Cases,1)
  dev.off()
png 
  2 
  trainingSize = 60
  ASEHolder1 = numeric()
  ASEHolder2 = numeric()
  ASEHolder3 = numeric()
  ASEHolder4 = numeric()
  ASEHolder5 = numeric()
  ASEHolder6 = numeric()
  ASEHolder7 = numeric()
  ASEHolder8 = numeric()
  ASEHolder9 = numeric()
  ASEHolder10 = numeric()
  ASEHolder11 = numeric()
  ASEHolder12 = numeric()
    
  for( k in 1:(84-(trainingSize + j) + 1))
  {
    sink("file")
    model1 = invisible(aic.wge(temp2[k:(k+(trainingSize-1-1))],type="aic"))
    model1_est = invisible(est.arma.wge(temp2[k:(k+(trainingSize-1-1))],p=model1$p,q=model1$q))
    forecasts = fore.aruma.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],phi = model1_est$phi, theta = model1_est$theta, s = 0, d = 1,n.ahead = j,plot=FALSE)
    ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - forecasts$f[1:1])^2)
    ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - forecasts$f[1:2])^2)
    ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - forecasts$f[1:3])^2)
    ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - forecasts$f[1:4])^2)
    ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - forecasts$f[1:5])^2)
    ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - forecasts$f[1:6])^2)
    ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - forecasts$f[1:7])^2)
    ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - forecasts$f[1:8])^2)
    ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - forecasts$f[1:9])^2)
    ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - forecasts$f[1:10])^2)
    ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - forecasts$f[1:11])^2)
    ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - forecasts$f[1:12])^2)
    sink()
    
    assign(paste("ARIMA_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - forecasts$f)^2)

  }
  
  WindowedASE1 = mean(ASEHolder1)
  WindowedASE2 = mean(ASEHolder2)
  WindowedASE3 = mean(ASEHolder3)
  WindowedASE4 = mean(ASEHolder4)
  WindowedASE5 = mean(ASEHolder5)
  WindowedASE6 = mean(ASEHolder6)
  WindowedASE7 = mean(ASEHolder7)
  WindowedASE8 = mean(ASEHolder8)
  WindowedASE9 = mean(ASEHolder9)
  WindowedASE10 = mean(ASEHolder10)
  WindowedASE11 = mean(ASEHolder11)
  WindowedASE12 = mean(ASEHolder12)
  results[i,paste0("ARIMA_1_ASE")] = WindowedASE1
  results[i,paste0("ARIMA_2_ASE")] = WindowedASE2
  results[i,paste0("ARIMA_3_ASE")] = WindowedASE3
  results[i,paste0("ARIMA_4_ASE")] = WindowedASE4
  results[i,paste0("ARIMA_5_ASE")] = WindowedASE5
  results[i,paste0("ARIMA_6_ASE")] = WindowedASE6
  results[i,paste0("ARIMA_7_ASE")] = WindowedASE7
  results[i,paste0("ARIMA_8_ASE")] = WindowedASE8
  results[i,paste0("ARIMA_9_ASE")] = WindowedASE9
  results[i,paste0("ARIMA_10_ASE")] = WindowedASE10
  results[i,paste0("ARIMA_11_ASE")] = WindowedASE11
  results[i,paste0("ARIMA_12_ASE")] = WindowedASE12
  results[i,paste0("ARIMA_F1")] = forecasts$f[1]  
  results[i,paste0("ARIMA_F2")] = forecasts$f[2]   
  results[i,paste0("ARIMA_F3")] = forecasts$f[3]   
  results[i,paste0("ARIMA_F4")] = forecasts$f[4]   
  results[i,paste0("ARIMA_F5")] = forecasts$f[5]   
  results[i,paste0("ARIMA_F6")] = forecasts$f[6]   
  results[i,paste0("ARIMA_F7")] = forecasts$f[7]   
  results[i,paste0("ARIMA_F8")] = forecasts$f[8]   
  results[i,paste0("ARIMA_F9")] = forecasts$f[9]   
  results[i,paste0("ARIMA_F10")] = forecasts$f[10]   
  results[i,paste0("ARIMA_F11")] = forecasts$f[11]   
  results[i,paste0("ARIMA_F12")] = forecasts$f[12]

  
 
#ARIMA Model with q=0 and S=12
  nulldev()
  temp2 = artrans.wge(temp1$STD_Cases,phi.tr=c(rep(0,11),1))
  dev.off()
png 
  2 
  trainingSize = 60
  ASEHolder1 = numeric()
  ASEHolder2 = numeric()
  ASEHolder3 = numeric()
  ASEHolder4 = numeric()
  ASEHolder5 = numeric()
  ASEHolder6 = numeric()
  ASEHolder7 = numeric()
  ASEHolder8 = numeric()
  ASEHolder9 = numeric()
  ASEHolder10 = numeric()
  ASEHolder11 = numeric()
  ASEHolder12 = numeric()
  
  for( k in 1:(84-(trainingSize + j) + 1))
  {
    sink("file")
    model1 = invisible(aic.wge(temp2[k:(k+(trainingSize-1-12))],q=0, type="aic"))
    if (model1$p == 0){
      newphi = 1
    } else {
      newphi = model1$p
    } 
    model1_est = invisible(est.ar.wge(temp2[k:(k+(trainingSize-1-12))],p=newphi))
    forecasts = fore.aruma.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],phi = model1_est$phi, theta = 0, s = 12, d = 0,n.ahead = j,plot=FALSE)
    ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - forecasts$f[1:1])^2)
    ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - forecasts$f[1:2])^2)
    ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - forecasts$f[1:3])^2)
    ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - forecasts$f[1:4])^2)
    ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - forecasts$f[1:5])^2)
    ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - forecasts$f[1:6])^2)
    ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - forecasts$f[1:7])^2)
    ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - forecasts$f[1:8])^2)
    ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - forecasts$f[1:9])^2)
    ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - forecasts$f[1:10])^2)
    ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - forecasts$f[1:11])^2)
    ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - forecasts$f[1:12])^2)
    sink()
    
    assign(paste("ARIS_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - forecasts$f)^2)
    assign(paste("ARIS_DF_",k,sep=""),trainingSize-(newphi+1))

  }
  
  WindowedASE1 = mean(ASEHolder1)
  WindowedASE2 = mean(ASEHolder2)
  WindowedASE3 = mean(ASEHolder3)
  WindowedASE4 = mean(ASEHolder4)
  WindowedASE5 = mean(ASEHolder5)
  WindowedASE6 = mean(ASEHolder6)
  WindowedASE7 = mean(ASEHolder7)
  WindowedASE8 = mean(ASEHolder8)
  WindowedASE9 = mean(ASEHolder9)
  WindowedASE10 = mean(ASEHolder10)
  WindowedASE11 = mean(ASEHolder11)
  WindowedASE12 = mean(ASEHolder12)
  results[i,paste0("ARI_S12_1_ASE")] = WindowedASE1
  results[i,paste0("ARI_S12_2_ASE")] = WindowedASE2
  results[i,paste0("ARI_S12_3_ASE")] = WindowedASE3
  results[i,paste0("ARI_S12_4_ASE")] = WindowedASE4
  results[i,paste0("ARI_S12_5_ASE")] = WindowedASE5
  results[i,paste0("ARI_S12_6_ASE")] = WindowedASE6
  results[i,paste0("ARI_S12_7_ASE")] = WindowedASE7
  results[i,paste0("ARI_S12_8_ASE")] = WindowedASE8
  results[i,paste0("ARI_S12_9_ASE")] = WindowedASE9
  results[i,paste0("ARI_S12_10_ASE")] = WindowedASE10
  results[i,paste0("ARI_S12_11_ASE")] = WindowedASE11
  results[i,paste0("ARI_S12_12_ASE")] = WindowedASE12
  results[i,paste0("ARI_S12_F1")] = forecasts$f[1]  
  results[i,paste0("ARI_S12_F2")] = forecasts$f[2]   
  results[i,paste0("ARI_S12_F3")] = forecasts$f[3]   
  results[i,paste0("ARI_S12_F4")] = forecasts$f[4]   
  results[i,paste0("ARI_S12_F5")] = forecasts$f[5]   
  results[i,paste0("ARI_S12_F6")] = forecasts$f[6]   
  results[i,paste0("ARI_S12_F7")] = forecasts$f[7]   
  results[i,paste0("ARI_S12_F8")] = forecasts$f[8]   
  results[i,paste0("ARI_S12_F9")] = forecasts$f[9]   
  results[i,paste0("ARI_S12_F10")] = forecasts$f[10]   
  results[i,paste0("ARI_S12_F11")] = forecasts$f[11]   
  results[i,paste0("ARI_S12_F12")] = forecasts$f[12]   

  
  
  #ARIMA Model with S=12
  nulldev()
  temp2 = artrans.wge(temp1$STD_Cases,phi.tr=c(rep(0,11),1))
  dev.off()
png 
  2 
  trainingSize = 60
  ASEHolder1 = numeric()
  ASEHolder2 = numeric()
  ASEHolder3 = numeric()
  ASEHolder4 = numeric()
  ASEHolder5 = numeric()
  ASEHolder6 = numeric()
  ASEHolder7 = numeric()
  ASEHolder8 = numeric()
  ASEHolder9 = numeric()
  ASEHolder10 = numeric()
  ASEHolder11 = numeric()
  ASEHolder12 = numeric()
  
  for( k in 1:(84-(trainingSize + j) + 1))
  {
    sink("file")
    model1 = invisible(aic.wge(temp2[k:(k+(trainingSize-1-12))],type="aic"))
    model1_est = invisible(est.arma.wge(temp2[k:(k+(trainingSize-1-12))],p=model1$p,q=model1$q))
    forecasts = fore.aruma.wge(temp1$STD_Cases[k:(k+(trainingSize-1))],phi = model1_est$phi, theta = model1_est$theta, s = 12, d = 0,n.ahead = j,plot=FALSE)
    ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - forecasts$f[1:1])^2)
    ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - forecasts$f[1:2])^2)
    ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - forecasts$f[1:3])^2)
    ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - forecasts$f[1:4])^2)
    ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - forecasts$f[1:5])^2)
    ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - forecasts$f[1:6])^2)
    ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - forecasts$f[1:7])^2)
    ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - forecasts$f[1:8])^2)
    ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - forecasts$f[1:9])^2)
    ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - forecasts$f[1:10])^2)
    ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - forecasts$f[1:11])^2)
    ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - forecasts$f[1:12])^2)
    sink()
    
    assign(paste("ARIMAS_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - forecasts$f)^2)

  }
  
  WindowedASE1 = mean(ASEHolder1)
  WindowedASE2 = mean(ASEHolder2)
  WindowedASE3 = mean(ASEHolder3)
  WindowedASE4 = mean(ASEHolder4)
  WindowedASE5 = mean(ASEHolder5)
  WindowedASE6 = mean(ASEHolder6)
  WindowedASE7 = mean(ASEHolder7)
  WindowedASE8 = mean(ASEHolder8)
  WindowedASE9 = mean(ASEHolder9)
  WindowedASE10 = mean(ASEHolder10)
  WindowedASE11 = mean(ASEHolder11)
  WindowedASE12 = mean(ASEHolder12)
  results[i,paste0("ARIMA_S12_1_ASE")] = WindowedASE1
  results[i,paste0("ARIMA_S12_2_ASE")] = WindowedASE2
  results[i,paste0("ARIMA_S12_3_ASE")] = WindowedASE3
  results[i,paste0("ARIMA_S12_4_ASE")] = WindowedASE4
  results[i,paste0("ARIMA_S12_5_ASE")] = WindowedASE5
  results[i,paste0("ARIMA_S12_6_ASE")] = WindowedASE6
  results[i,paste0("ARIMA_S12_7_ASE")] = WindowedASE7
  results[i,paste0("ARIMA_S12_8_ASE")] = WindowedASE8
  results[i,paste0("ARIMA_S12_9_ASE")] = WindowedASE9
  results[i,paste0("ARIMA_S12_10_ASE")] = WindowedASE10
  results[i,paste0("ARIMA_S12_11_ASE")] = WindowedASE11
  results[i,paste0("ARIMA_S12_12_ASE")] = WindowedASE12
  results[i,paste0("ARIMA_S12_F1")] = forecasts$f[1]  
  results[i,paste0("ARIMA_S12_F2")] = forecasts$f[2]   
  results[i,paste0("ARIMA_S12_F3")] = forecasts$f[3]   
  results[i,paste0("ARIMA_S12_F4")] = forecasts$f[4]   
  results[i,paste0("ARIMA_S12_F5")] = forecasts$f[5]   
  results[i,paste0("ARIMA_S12_F6")] = forecasts$f[6]   
  results[i,paste0("ARIMA_S12_F7")] = forecasts$f[7]   
  results[i,paste0("ARIMA_S12_F8")] = forecasts$f[8]   
  results[i,paste0("ARIMA_S12_F9")] = forecasts$f[9]   
  results[i,paste0("ARIMA_S12_F10")] = forecasts$f[10]   
  results[i,paste0("ARIMA_S12_F11")] = forecasts$f[11]   
  results[i,paste0("ARIMA_S12_F12")] = forecasts$f[12]   

  
  
  #Random Forest
  trainingSize = 60
  ASEHolder1 = numeric()
  ASEHolder2 = numeric()
  ASEHolder3 = numeric()
  ASEHolder4 = numeric()
  ASEHolder5 = numeric()
  ASEHolder6 = numeric()
  ASEHolder7 = numeric()
  ASEHolder8 = numeric()
  ASEHolder9 = numeric()
  ASEHolder10 = numeric()
  ASEHolder11 = numeric()
  ASEHolder12 = numeric()
  
  for( k in 1:(84-(trainingSize + j) + 1))
  {
    sink("file")
   
    forecasts <- rf_ts(j, temp1[k:(k+(trainingSize-1)),], FALSE)
    
    ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - forecasts$forecast[1:1])^2)
    ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - forecasts$forecast[1:2])^2)
    ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - forecasts$forecast[1:3])^2)
    ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - forecasts$forecast[1:4])^2)
    ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - forecasts$forecast[1:5])^2)
    ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - forecasts$forecast[1:6])^2)
    ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - forecasts$forecast[1:7])^2)
    ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - forecasts$forecast[1:8])^2)
    ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - forecasts$forecast[1:9])^2)
    ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - forecasts$forecast[1:10])^2)
    ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - forecasts$forecast[1:11])^2)
    ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - forecasts$forecast[1:12])^2)
    sink()
    
    assign(paste("RF_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - forecasts$forecast)^2)

  }
  
  WindowedASE1 = mean(ASEHolder1)
  WindowedASE2 = mean(ASEHolder2)
  WindowedASE3 = mean(ASEHolder3)
  WindowedASE4 = mean(ASEHolder4)
  WindowedASE5 = mean(ASEHolder5)
  WindowedASE6 = mean(ASEHolder6)
  WindowedASE7 = mean(ASEHolder7)
  WindowedASE8 = mean(ASEHolder8)
  WindowedASE9 = mean(ASEHolder9)
  WindowedASE10 = mean(ASEHolder10)
  WindowedASE11 = mean(ASEHolder11)
  WindowedASE12 = mean(ASEHolder12)
  results[i,paste0("RF_1_ASE")] = WindowedASE1
  results[i,paste0("RF_2_ASE")] = WindowedASE2
  results[i,paste0("RF_3_ASE")] = WindowedASE3
  results[i,paste0("RF_4_ASE")] = WindowedASE4
  results[i,paste0("RF_5_ASE")] = WindowedASE5
  results[i,paste0("RF_6_ASE")] = WindowedASE6
  results[i,paste0("RF_7_ASE")] = WindowedASE7
  results[i,paste0("RF_8_ASE")] = WindowedASE8
  results[i,paste0("RF_9_ASE")] = WindowedASE9
  results[i,paste0("RF_10_ASE")] = WindowedASE10
  results[i,paste0("RF_11_ASE")] = WindowedASE11
  results[i,paste0("RF_12_ASE")] = WindowedASE12
  results[i,paste0("RF_F1")] = forecasts$forecast[1]  
  results[i,paste0("RF_F2")] = forecasts$forecast[2]   
  results[i,paste0("RF_F3")] = forecasts$forecast[3]   
  results[i,paste0("RF_F4")] = forecasts$forecast[4]   
  results[i,paste0("RF_F5")] = forecasts$forecast[5]   
  results[i,paste0("RF_F6")] = forecasts$forecast[6]   
  results[i,paste0("RF_F7")] = forecasts$forecast[7]   
  results[i,paste0("RF_F8")] = forecasts$forecast[8]   
  results[i,paste0("RF_F9")] = forecasts$forecast[9]   
  results[i,paste0("RF_F10")] = forecasts$forecast[10]   
  results[i,paste0("RF_F11")] = forecasts$forecast[11]   
  results[i,paste0("RF_F12")] = forecasts$forecast[12]   

  
  
  # MLP
  trainingSize = 60
  ASEHolder1 = numeric()
  ASEHolder2 = numeric()
  ASEHolder3 = numeric()
  ASEHolder4 = numeric()
  ASEHolder5 = numeric()
  ASEHolder6 = numeric()
  ASEHolder7 = numeric()
  ASEHolder8 = numeric()
  ASEHolder9 = numeric()
  ASEHolder10 = numeric()
  ASEHolder11 = numeric()
  ASEHolder12 = numeric()
  
  for( k in 1:(84-(trainingSize + j) + 1))
  {
    sink("file")

    forecasts <- nnc(temp1$STD_Cases[k:(k+(trainingSize-1))], j, 10, c(5, 10, 15, 5), FALSE)
    
    ASEHolder1[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 1 - 1)] - forecasts$forecast[1:1])^2)
    ASEHolder2[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 2 - 1)] - forecasts$forecast[1:2])^2)
    ASEHolder3[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 3 - 1)] - forecasts$forecast[1:3])^2)
    ASEHolder4[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 4 - 1)] - forecasts$forecast[1:4])^2)
    ASEHolder5[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 5 - 1)] - forecasts$forecast[1:5])^2)
    ASEHolder6[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 6 - 1)] - forecasts$forecast[1:6])^2)
    ASEHolder7[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 7 - 1)] - forecasts$forecast[1:7])^2)
    ASEHolder8[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 8 - 1)] - forecasts$forecast[1:8])^2)
    ASEHolder9[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 9 - 1)] - forecasts$forecast[1:9])^2)
    ASEHolder10[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 10 - 1)] - forecasts$forecast[1:10])^2)
    ASEHolder11[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 11 - 1)] - forecasts$forecast[1:11])^2)
    ASEHolder12[k] = mean((temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + 12 - 1)] - forecasts$forecast[1:12])^2)
    sink()
    
    assign(paste("MLP_Results_",k,sep=""),(temp1$STD_Cases[(trainingSize+k):(trainingSize+ k + j - 1)] - forecasts$forecast)^2)

  }
  
  WindowedASE1 = mean(ASEHolder1)
  WindowedASE2 = mean(ASEHolder2)
  WindowedASE3 = mean(ASEHolder3)
  WindowedASE4 = mean(ASEHolder4)
  WindowedASE5 = mean(ASEHolder5)
  WindowedASE6 = mean(ASEHolder6)
  WindowedASE7 = mean(ASEHolder7)
  WindowedASE8 = mean(ASEHolder8)
  WindowedASE9 = mean(ASEHolder9)
  WindowedASE10 = mean(ASEHolder10)
  WindowedASE11 = mean(ASEHolder11)
  WindowedASE12 = mean(ASEHolder12)
  results[i,paste0("MLP_1_ASE")] = WindowedASE1
  results[i,paste0("MLP_2_ASE")] = WindowedASE2
  results[i,paste0("MLP_3_ASE")] = WindowedASE3
  results[i,paste0("MLP_4_ASE")] = WindowedASE4
  results[i,paste0("MLP_5_ASE")] = WindowedASE5
  results[i,paste0("MLP_6_ASE")] = WindowedASE6
  results[i,paste0("MLP_7_ASE")] = WindowedASE7
  results[i,paste0("MLP_8_ASE")] = WindowedASE8
  results[i,paste0("MLP_9_ASE")] = WindowedASE9
  results[i,paste0("MLP_10_ASE")] = WindowedASE10
  results[i,paste0("MLP_11_ASE")] = WindowedASE11
  results[i,paste0("MLP_12_ASE")] = WindowedASE12
  results[i,paste0("MLP_F1")] = forecasts$forecast[1]  
  results[i,paste0("MLP_F2")] = forecasts$forecast[2]   
  results[i,paste0("MLP_F3")] = forecasts$forecast[3]   
  results[i,paste0("MLP_F4")] = forecasts$forecast[4]   
  results[i,paste0("MLP_F5")] = forecasts$forecast[5]   
  results[i,paste0("MLP_F6")] = forecasts$forecast[6]   
  results[i,paste0("MLP_F7")] = forecasts$forecast[7]   
  results[i,paste0("MLP_F8")] = forecasts$forecast[8]   
  results[i,paste0("MLP_F9")] = forecasts$forecast[9]   
  results[i,paste0("MLP_F10")] = forecasts$forecast[10]   
  results[i,paste0("MLP_F11")] = forecasts$forecast[11]   
  results[i,paste0("MLP_F12")] = forecasts$forecast[12]   

  
  results[i,paste0("ACTUAL_1")] = temp1$STD_Cases[73]
  results[i,paste0("ACTUAL_2")] = temp1$STD_Cases[74]
  results[i,paste0("ACTUAL_3")] = temp1$STD_Cases[75]
  results[i,paste0("ACTUAL_4")] = temp1$STD_Cases[76]
  results[i,paste0("ACTUAL_5")] = temp1$STD_Cases[77]
  results[i,paste0("ACTUAL_6")] = temp1$STD_Cases[78]
  results[i,paste0("ACTUAL_7")] = temp1$STD_Cases[79]
  results[i,paste0("ACTUAL_8")] = temp1$STD_Cases[80]
  results[i,paste0("ACTUAL_9")] = temp1$STD_Cases[81]
  results[i,paste0("ACTUAL_10")] = temp1$STD_Cases[82]
  results[i,paste0("ACTUAL_11")] = temp1$STD_Cases[83]
  results[i,paste0("ACTUAL_12")] = temp1$STD_Cases[84]

  
  #graph ASEs for each Model
  EqualMeans_Results <- rbind(EqualMeans_Results_1,EqualMeans_Results_2,EqualMeans_Results_3,EqualMeans_Results_4,EqualMeans_Results_5,EqualMeans_Results_6,
                              EqualMeans_Results_7,EqualMeans_Results_8,EqualMeans_Results_9,EqualMeans_Results_10,EqualMeans_Results_11,EqualMeans_Results_12,
                              EqualMeans_Results_13)
  
  AR_Results <- rbind(AR_Results_1,AR_Results_2,AR_Results_3,AR_Results_4,AR_Results_5,AR_Results_6,AR_Results_7,AR_Results_8,AR_Results_9,AR_Results_10,
                      AR_Results_11,AR_Results_12,AR_Results_13)
  
  ARMA_Results <- rbind(ARMA_Results_1,ARMA_Results_2,ARMA_Results_3,ARMA_Results_4,ARMA_Results_5,ARMA_Results_6,ARMA_Results_7,ARMA_Results_8,
                       ARMA_Results_9,ARMA_Results_10,ARMA_Results_11,ARMA_Results_12,ARMA_Results_13)

  ARI_Results <- rbind(ARI_Results_1,ARI_Results_2,ARI_Results_3,ARI_Results_4,ARI_Results_5,ARI_Results_6,ARI_Results_7,ARI_Results_8,
                         ARI_Results_9,ARI_Results_10,ARI_Results_11,ARI_Results_12,ARI_Results_13)
 
  ARIMA_Results <- rbind(ARIMA_Results_1,ARIMA_Results_2,ARIMA_Results_3,ARIMA_Results_4,ARIMA_Results_5,ARIMA_Results_6,ARIMA_Results_7,ARIMA_Results_8,
                         ARIMA_Results_9,ARIMA_Results_10,ARIMA_Results_11,ARIMA_Results_12,ARIMA_Results_13)
      
  ARIS_Results <- rbind(ARIS_Results_1,ARIS_Results_2,ARIS_Results_3,ARIS_Results_4,ARIS_Results_5,ARIS_Results_6,ARIS_Results_7,ARIS_Results_8,
                          ARIS_Results_9,ARIS_Results_10,ARIS_Results_11,ARIS_Results_12,ARIS_Results_13)
  
  ARIMAS_Results <- rbind(ARIMAS_Results_1,ARIMAS_Results_2,ARIMAS_Results_3,ARIMAS_Results_4,ARIMAS_Results_5,ARIMAS_Results_6,ARIMAS_Results_7,ARIMAS_Results_8,
                          ARIMAS_Results_9,ARIMAS_Results_10,ARIMAS_Results_11,ARIMAS_Results_12,ARIMAS_Results_13)
  
  RF_Results <- rbind(RF_Results_1,RF_Results_2,RF_Results_3,RF_Results_4,RF_Results_5,RF_Results_6,RF_Results_7,RF_Results_8,
                        RF_Results_9,RF_Results_10,RF_Results_11,RF_Results_12,RF_Results_13)
    
  MLP_Results <- rbind(MLP_Results_1,MLP_Results_2,MLP_Results_3,MLP_Results_4,MLP_Results_5,MLP_Results_6,MLP_Results_7,MLP_Results_8,
                      MLP_Results_9,MLP_Results_10,MLP_Results_11,MLP_Results_12,MLP_Results_13)
      
  EqualMeans_Means <- colMeans(EqualMeans_Results)
  AR_Means <- colMeans(AR_Results)
  ARMA_Means <- colMeans(ARMA_Results)
  ARI_Means <- colMeans(ARI_Results)
  ARIMA_Means <- colMeans(ARIMA_Results)
  ARIS_Means <- colMeans(ARIS_Results)
  ARIMAS_Means <- colMeans(ARIMAS_Results)
  RF_Means <- colMeans(RF_Results)
  MLP_Means <- colMeans(MLP_Results)
  Combined_Means <- data.frame(EqualMeans_Means,AR_Means, ARMA_Means, ARI_Means, ARIMA_Means, ARIS_Means, ARIMAS_Means,RF_Means,MLP_Means)
  Combined_Means$horizon <- as.numeric(row.names(Combined_Means))
  
# more colors #73EBAE
  g <- ggplot(data=Combined_Means, aes(horizon)) +
    geom_line(aes(y=EqualMeans_Means, color="Equal Means"),size=1.5) +
    geom_line(aes(y=AR_Means, color="AR"),size=1.5) +
    geom_line(aes(y=ARMA_Means, color="ARMA"),size=1.5) +
    geom_line(aes(y=ARI_Means, color="AR with d=1"),size=1.5) +
    geom_line(aes(y=ARIMA_Means, color="ARIMA with d=1"),size=1.5) +
    geom_line(aes(y=ARIS_Means, color="AR with s=12"),size=1.5) +
    geom_line(aes(y=ARIMAS_Means, color="ARIMA with d=0, s=12"),size=1.5) +
    geom_line(aes(y=RF_Means, color="Random Forest"),size=1.5) +
    geom_line(aes(y=MLP_Means, color="MLP"),size=1.5) +
    scale_color_manual(values = c(
      'Equal Means' = '#004159',
      'AR' = '#65A8C4',
      'ARMA' = '#8C65D3',
      'AR with d=1' = '#9A93EC',
      'ARIMA with d=1' = '#0052A5',
      'AR with s=12' = '#413BF7',
      'ARIMA with d=0, s=12' = '#00ADCE',
      'Random Forest' = '#59DBF1',
      'MLP' = '#00C590'
    )) +
    labs(color='Models') +
    scale_x_continuous(breaks=seq(0,13,1)) +
    ggtitle(paste("Model ASEs for ", product,"and Customer",customer)) +
    xlab("Month Ahead Forecast") +
    ylab("ASE") +
    theme(panel.background = element_blank(), axis.line = element_line(colour = "black"), legend.title = element_blank())
  
  print(g)

# f-statistic calculations
  EqualMeans_DF <- rbind(EqualMeans_DF_1,EqualMeans_DF_2,EqualMeans_DF_3,EqualMeans_DF_4,EqualMeans_DF_5,EqualMeans_DF_6,EqualMeans_DF_7,
                         EqualMeans_DF_8,EqualMeans_DF_9,EqualMeans_DF_10,EqualMeans_DF_11,EqualMeans_DF_12,EqualMeans_DF_13)
  
  AR_DF <- rbind(AR_DF_1,AR_DF_2,AR_DF_3,AR_DF_4,AR_DF_5,AR_DF_6,AR_DF_7,AR_DF_8,AR_DF_9,AR_DF_10,AR_DF_11,AR_DF_12,AR_DF_13)
  
  ARI_DF <- rbind(ARI_DF_1,ARI_DF_2,ARI_DF_3,ARI_DF_4,ARI_DF_5,ARI_DF_6,ARI_DF_7,ARI_DF_8,ARI_DF_9,ARI_DF_10,ARI_DF_11,ARI_DF_12,ARI_DF_13)
  
  ARIS_DF <- rbind(ARIS_DF_1,ARIS_DF_2,ARIS_DF_3,ARIS_DF_4,ARIS_DF_5,ARIS_DF_6,ARIS_DF_7,ARIS_DF_8,ARIS_DF_9,ARIS_DF_10,ARIS_DF_11,ARIS_DF_12,ARIS_DF_13)
  
  
  EqualMeans_Results <- rbind(sum(EqualMeans_Results_1),sum(EqualMeans_Results_2),sum(EqualMeans_Results_3),sum(EqualMeans_Results_4),sum(EqualMeans_Results_5),
                              sum(EqualMeans_Results_6),sum(EqualMeans_Results_7),sum(EqualMeans_Results_8),sum(EqualMeans_Results_9),sum(EqualMeans_Results_10),
                              sum(EqualMeans_Results_11),sum(EqualMeans_Results_12),sum(EqualMeans_Results_13))
  
  AR_Results <- rbind(sum(AR_Results_1),sum(AR_Results_2),sum(AR_Results_3),sum(AR_Results_4),sum(AR_Results_5),sum(AR_Results_6),sum(AR_Results_7),
                      sum(AR_Results_8),sum(AR_Results_9),sum(AR_Results_10),sum(AR_Results_11),sum(AR_Results_12),sum(AR_Results_13))
  
  ARI_Results <- rbind(sum(ARI_Results_1),sum(ARI_Results_2),sum(ARI_Results_3),sum(ARI_Results_4),sum(ARI_Results_5),sum(ARI_Results_6),sum(ARI_Results_7),
                       sum(ARI_Results_8),sum(ARI_Results_9),sum(ARI_Results_10),sum(ARI_Results_11),sum(ARI_Results_12),sum(ARI_Results_13))
  
  ARIS_Results <- rbind(sum(ARIS_Results_1),sum(ARIS_Results_2),sum(ARIS_Results_3),sum(ARIS_Results_4),sum(ARIS_Results_5),sum(ARIS_Results_6),sum(ARIS_Results_7),
                       sum(ARIS_Results_8),sum(ARIS_Results_9),sum(ARIS_Results_10),sum(ARIS_Results_11),sum(ARIS_Results_12),sum(ARIS_Results_13))
  
  df_model = EqualMeans_DF - AR_DF
  ss_model = EqualMeans_Results - AR_Results
  ms_model = ss_model/df_model
  ms_ar = AR_Results/AR_DF
  F = ms_model/ms_ar
  AR_p_value = pf(F,df_model,AR_DF,lower.tail=FALSE)
  AR_p_tally = sum(AR_p_value[,1]<.05)
  results[i,"AR_F_Tally"] = AR_p_tally
  
  if (AR_p_tally >= 9){
    results[i,"AR_F_Conclusion"] = "Different"
  } else if (AR_p_tally <= 4){
    results[i,"AR_F_Conclusion"] = "Same"
  } else {
     results[i,"AR_F_Conclusion"] = "Inconclusive"
  }

  df_model = EqualMeans_DF - ARI_DF
  ss_model = EqualMeans_Results - ARI_Results
  ms_model = ss_model/df_model
  ms_ari = ARI_Results/ARI_DF
  F = ms_model/ms_ari
  ARI_p_value = pf(F,df_model,ARI_DF,lower.tail=FALSE)
  ARI_p_tally = sum(ARI_p_value[,1]<.05)
  results[i,"ARI_F_Tally"] = ARI_p_tally
  
  if (ARI_p_tally >= 9){
    results[i,"ARI_F_Conclusion"] = "Different"
  } else if (ARI_p_tally <= 4){
    results[i,"ARI_F_Conclusion"] = "Same"
  } else {
    results[i,"ARI_F_Conclusion"] = "Inconclusive"
  }

  df_model = EqualMeans_DF - ARIS_DF
  ss_model = EqualMeans_Results - ARIS_Results
  ms_model = ss_model/df_model
  ms_aris = ARIS_Results/ARIS_DF
  F = ms_model/ms_aris
  ARIS_p_value = pf(F,df_model,ARIS_DF,lower.tail=FALSE)
  ARIS_p_tally = sum(ARIS_p_value[,1]<.05)
  results[i,"ARIS_F_Tally"] = ARIS_p_tally
  
  if (ARIS_p_tally >= 9){
    results[i,"ARIS_F_Conclusion"] = "Different"
  } else if (ARIS_p_tally <= 4){
    results[i,"ARIS_F_Conclusion"] = "Same"
  } else {
     results[i,"ARIS_F_Conclusion"] = "Inconclusive"
  }

results$winning_1 <- colnames(results[c("EqualMeans_1_ASE","AR_1_ASE","ARMA_1_ASE","ARI_1_ASE","ARIMA_1_ASE","ARI_S12_1_ASE","ARIMA_S12_1_ASE","RF_1_ASE","MLP_1_ASE")])[apply(results[c("EqualMeans_1_ASE","AR_1_ASE","ARMA_1_ASE","ARI_1_ASE","ARIMA_1_ASE","ARI_S12_1_ASE","ARIMA_S12_1_ASE","RF_1_ASE","MLP_1_ASE")],1,which.min)]

results$winning_2 <- colnames(results[c("EqualMeans_2_ASE","AR_2_ASE","ARMA_2_ASE","ARI_2_ASE","ARIMA_2_ASE","ARI_S12_2_ASE","ARIMA_S12_2_ASE","RF_2_ASE","MLP_2_ASE")])[apply(results[c("EqualMeans_2_ASE","AR_2_ASE","ARMA_2_ASE","ARI_2_ASE","ARIMA_2_ASE","ARI_S12_2_ASE","ARIMA_S12_2_ASE","RF_2_ASE","MLP_2_ASE")],1,which.min)]

results$winning_3 <- colnames(results[c("EqualMeans_3_ASE","AR_3_ASE","ARMA_3_ASE","ARI_3_ASE","ARIMA_3_ASE","ARI_S12_3_ASE","ARIMA_S12_3_ASE","RF_3_ASE","MLP_3_ASE")])[apply(results[c("EqualMeans_3_ASE","AR_3_ASE","ARMA_3_ASE","ARI_3_ASE","ARIMA_3_ASE","ARI_S12_3_ASE","ARIMA_S12_3_ASE","RF_3_ASE","MLP_3_ASE")],1,which.min)]

results$winning_4 <- colnames(results[c("EqualMeans_4_ASE","AR_4_ASE","ARMA_4_ASE","ARI_4_ASE","ARIMA_4_ASE","ARI_S12_4_ASE","ARIMA_S12_4_ASE","RF_4_ASE","MLP_4_ASE")])[apply(results[c("EqualMeans_4_ASE","AR_4_ASE","ARMA_4_ASE","ARI_4_ASE","ARIMA_4_ASE","ARI_S12_4_ASE","ARIMA_S12_4_ASE","RF_4_ASE","MLP_4_ASE")],1,which.min)]

results$winning_5 <- colnames(results[c("EqualMeans_5_ASE","AR_5_ASE","ARMA_5_ASE","ARI_5_ASE","ARIMA_5_ASE","ARI_S12_5_ASE","ARIMA_S12_5_ASE","RF_5_ASE","MLP_5_ASE")])[apply(results[c("EqualMeans_5_ASE","AR_5_ASE","ARMA_5_ASE","ARI_5_ASE","ARIMA_5_ASE","ARI_S12_5_ASE","ARIMA_S12_5_ASE","RF_5_ASE","MLP_5_ASE")],1,which.min)]

results$winning_6 <- colnames(results[c("EqualMeans_6_ASE","AR_6_ASE","ARMA_6_ASE","ARI_6_ASE","ARIMA_6_ASE","ARI_S12_6_ASE","ARIMA_S12_6_ASE","RF_6_ASE","MLP_6_ASE")])[apply(results[c("EqualMeans_6_ASE","AR_6_ASE","ARMA_6_ASE","ARI_6_ASE","ARIMA_6_ASE","ARI_S12_6_ASE","ARIMA_S12_6_ASE","RF_6_ASE","MLP_6_ASE")],1,which.min)]

results$winning_7 <- colnames(results[c("EqualMeans_7_ASE","AR_7_ASE","ARMA_7_ASE","ARI_7_ASE","ARIMA_7_ASE","ARI_S12_7_ASE","ARIMA_S12_7_ASE","RF_7_ASE","MLP_7_ASE")])[apply(results[c("EqualMeans_7_ASE","AR_7_ASE","ARMA_7_ASE","ARI_7_ASE","ARIMA_7_ASE","ARI_S12_7_ASE","ARIMA_S12_7_ASE","RF_7_ASE","MLP_7_ASE")],1,which.min)]

results$winning_8 <- colnames(results[c("EqualMeans_8_ASE","AR_8_ASE","ARMA_8_ASE","ARI_8_ASE","ARIMA_8_ASE","ARI_S12_8_ASE","ARIMA_S12_8_ASE","RF_8_ASE","MLP_8_ASE")])[apply(results[c("EqualMeans_8_ASE","AR_8_ASE","ARMA_8_ASE","ARI_8_ASE","ARIMA_8_ASE","ARI_S12_8_ASE","ARIMA_S12_8_ASE","RF_8_ASE","MLP_8_ASE")],1,which.min)]

results$winning_9 <- colnames(results[c("EqualMeans_9_ASE","AR_9_ASE","ARMA_9_ASE","ARI_9_ASE","ARIMA_9_ASE","ARI_S12_9_ASE","ARIMA_S12_9_ASE","RF_9_ASE","MLP_9_ASE")])[apply(results[c("EqualMeans_9_ASE","AR_9_ASE","ARMA_9_ASE","ARI_9_ASE","ARIMA_9_ASE","ARI_S12_9_ASE","ARIMA_S12_9_ASE","RF_9_ASE","MLP_9_ASE")],1,which.min)]

results$winning_10 <- colnames(results[c("EqualMeans_10_ASE","AR_10_ASE","ARMA_10_ASE","ARI_10_ASE","ARIMA_10_ASE","ARI_S12_10_ASE","ARIMA_S12_10_ASE","RF_10_ASE","MLP_10_ASE")])[apply(results[c("EqualMeans_10_ASE","AR_10_ASE","ARMA_10_ASE","ARI_10_ASE","ARIMA_10_ASE","ARI_S12_10_ASE","ARIMA_S12_10_ASE","RF_10_ASE","MLP_10_ASE")],1,which.min)]

results$winning_11 <- colnames(results[c("EqualMeans_11_ASE","AR_11_ASE","ARMA_11_ASE","ARI_11_ASE","ARIMA_11_ASE","ARI_S12_11_ASE","ARIMA_S12_11_ASE","RF_11_ASE","MLP_11_ASE")])[apply(results[c("EqualMeans_11_ASE","AR_11_ASE","ARMA_11_ASE","ARI_11_ASE","ARIMA_11_ASE","ARI_S12_11_ASE","ARIMA_S12_11_ASE","RF_11_ASE","MLP_11_ASE")],1,which.min)]

results$winning_12 <- colnames(results[c("EqualMeans_12_ASE","AR_12_ASE","ARMA_12_ASE","ARI_12_ASE","ARIMA_12_ASE","ARI_S12_12_ASE","ARIMA_S12_12_ASE","RF_12_ASE","MLP_12_ASE")])[apply(results[c("EqualMeans_12_ASE","AR_12_ASE","ARMA_12_ASE","ARI_12_ASE","ARIMA_12_ASE","ARI_S12_12_ASE","ARIMA_S12_12_ASE","RF_12_ASE","MLP_12_ASE")],1,which.min)]

formattable(results, align = c("l", rep("r", NCOL(table_a) - 1)))
Product_Type Product Customer ljung_10 ljung_24 ljung_results top_5_bic ADF KPSS stationarity_results EqualMeans_1_ASE EqualMeans_2_ASE EqualMeans_3_ASE EqualMeans_4_ASE EqualMeans_5_ASE EqualMeans_6_ASE EqualMeans_7_ASE EqualMeans_8_ASE EqualMeans_9_ASE EqualMeans_10_ASE EqualMeans_11_ASE EqualMeans_12_ASE EqualMeans_F1 EqualMeans_F2 EqualMeans_F3 EqualMeans_F4 EqualMeans_F5 EqualMeans_F6 EqualMeans_F7 EqualMeans_F8 EqualMeans_F9 EqualMeans_F10 EqualMeans_F11 EqualMeans_F12 AR_1_ASE AR_2_ASE AR_3_ASE AR_4_ASE AR_5_ASE AR_6_ASE AR_7_ASE AR_8_ASE AR_9_ASE AR_10_ASE AR_11_ASE AR_12_ASE AR_F1 AR_F2 AR_F3 AR_F4 AR_F5 AR_F6 AR_F7 AR_F8 AR_F9 AR_F10 AR_F11 AR_F12 ARMA_1_ASE ARMA_2_ASE ARMA_3_ASE ARMA_4_ASE ARMA_5_ASE ARMA_6_ASE ARMA_7_ASE ARMA_8_ASE ARMA_9_ASE ARMA_10_ASE ARMA_11_ASE ARMA_12_ASE ARMA_F1 ARMA_F2 ARMA_F3 ARMA_F4 ARMA_F5 ARMA_F6 ARMA_F7 ARMA_F8 ARMA_F9 ARMA_F10 ARMA_F11 ARMA_F12 ARI_1_ASE ARI_2_ASE ARI_3_ASE ARI_4_ASE ARI_5_ASE ARI_6_ASE ARI_7_ASE ARI_8_ASE ARI_9_ASE ARI_10_ASE ARI_11_ASE ARI_12_ASE ARI_F1 ARI_F2 ARI_F3 ARI_F4 ARI_F5 ARI_F6 ARI_F7 ARI_F8 ARI_F9 ARI_F10 ARI_F11 ARI_F12 ARIMA_1_ASE ARIMA_2_ASE ARIMA_3_ASE ARIMA_4_ASE ARIMA_5_ASE ARIMA_6_ASE ARIMA_7_ASE ARIMA_8_ASE ARIMA_9_ASE ARIMA_10_ASE ARIMA_11_ASE ARIMA_12_ASE ARIMA_F1 ARIMA_F2 ARIMA_F3 ARIMA_F4 ARIMA_F5 ARIMA_F6 ARIMA_F7 ARIMA_F8 ARIMA_F9 ARIMA_F10 ARIMA_F11 ARIMA_F12 ARI_S12_1_ASE ARI_S12_2_ASE ARI_S12_3_ASE ARI_S12_4_ASE ARI_S12_5_ASE ARI_S12_6_ASE ARI_S12_7_ASE ARI_S12_8_ASE ARI_S12_9_ASE ARI_S12_10_ASE ARI_S12_11_ASE ARI_S12_12_ASE ARI_S12_F1 ARI_S12_F2 ARI_S12_F3 ARI_S12_F4 ARI_S12_F5 ARI_S12_F6 ARI_S12_F7 ARI_S12_F8 ARI_S12_F9 ARI_S12_F10 ARI_S12_F11 ARI_S12_F12 ARIMA_S12_1_ASE ARIMA_S12_2_ASE ARIMA_S12_3_ASE ARIMA_S12_4_ASE ARIMA_S12_5_ASE ARIMA_S12_6_ASE ARIMA_S12_7_ASE ARIMA_S12_8_ASE ARIMA_S12_9_ASE ARIMA_S12_10_ASE ARIMA_S12_11_ASE ARIMA_S12_12_ASE ARIMA_S12_F1 ARIMA_S12_F2 ARIMA_S12_F3 ARIMA_S12_F4 ARIMA_S12_F5 ARIMA_S12_F6 ARIMA_S12_F7 ARIMA_S12_F8 ARIMA_S12_F9 ARIMA_S12_F10 ARIMA_S12_F11 ARIMA_S12_F12 RF_1_ASE RF_2_ASE RF_3_ASE RF_4_ASE RF_5_ASE RF_6_ASE RF_7_ASE RF_8_ASE RF_9_ASE RF_10_ASE RF_11_ASE RF_12_ASE RF_F1 RF_F2 RF_F3 RF_F4 RF_F5 RF_F6 RF_F7 RF_F8 RF_F9 RF_F10 RF_F11 RF_F12 MLP_1_ASE MLP_2_ASE MLP_3_ASE MLP_4_ASE MLP_5_ASE MLP_6_ASE MLP_7_ASE MLP_8_ASE MLP_9_ASE MLP_10_ASE MLP_11_ASE MLP_12_ASE MLP_F1 MLP_F2 MLP_F3 MLP_F4 MLP_F5 MLP_F6 MLP_F7 MLP_F8 MLP_F9 MLP_F10 MLP_F11 MLP_F12 ACTUAL_1 ACTUAL_2 ACTUAL_3 ACTUAL_4 ACTUAL_5 ACTUAL_6 ACTUAL_7 ACTUAL_8 ACTUAL_9 ACTUAL_10 ACTUAL_11 ACTUAL_12 AR_F_Tally AR_F_Conclusion ARI_F_Tally ARI_F_Conclusion ARIS_F_Tally ARIS_F_Conclusion winning_1 winning_2 winning_3 winning_4 winning_5 winning_6 winning_7 winning_8 winning_9 winning_10 winning_11 winning_12
NA NA NA 2.322229e-06 1.124084e-05 not white noise NA 0.3279525 0.1 inconclusive 4059.231 3679.643 3401.196 3372.65 3330.088 3663.9 4022.845 4369.204 4647.175 4822.214 4991.421 5189.347 387.7917 387.7917 387.7917 387.7917 387.7917 387.7917 387.7917 387.7917 387.7917 387.7917 387.7917 387.7917 3173.814 3540.745 3475.842 3562.13 3495.253 3772.052 4094.861 4425.126 4696.629 4868.098 5034.353 5228.588 325.3383 350.9228 366.0264 374.9427 380.2064 383.3137 385.1482 386.2311 386.8704 387.2478 387.4706 387.6021 3173.814 3540.745 3475.842 3562.13 3495.253 3772.052 4094.861 4425.126 4696.629 4868.098 5034.353 5228.588 325.3383 350.9228 366.0264 374.9427 380.2064 383.3137 385.1482 386.2311 386.8704 387.2478 387.4706 387.6021 2805.987 3483.409 3535.384 3752.884 3647.365 3630.66 3793.221 4139.752 4570.513 4915.069 5202.2 5361.336 306.5299 334.733 353.8968 354.5872 338.8502 330.6731 329.709 334.0052 339.2221 339.8121 338.2444 336.3196 7105.365 12887.81 15588.65 18324.48 19097.58 18725.51 18836.91 20251.35 21113.27 21670.1 21527.4 20880.61 244.7304 221.902 207.9192 199.3544 194.1084 190.8951 188.9268 187.7213 186.9828 186.5305 186.2535 186.0838 8930.775 9357.545 10147.48 9999.186 9650.684 9565.89 9653.465 9851.987 10122.16 10246.46 10192.57 10146.67 416.2036 403.062 299.9213 407.1609 345.28 354.6572 399.4513 418.6447 443.691 404.1049 331.5171 281.7067 7755.406 8228.346 9375.721 9464.392 9215.362 9205.438 9316.413 9585.313 9869.667 10090.96 10043.93 9989.717 416.2036 403.062 299.9213 407.1609 345.28 354.6572 399.4513 418.6447 443.691 404.1049 331.5171 281.7067 6542.481 6435.333 6151.311 6122.353 5961.048 6014.357 6177.089 6448.883 6751.558 6914.489 6926.439 6936.8 442.075 440.7919 350.4793 413.5456 338.6639 343.1636 406.4955 420.4103 434.264 426.1187 329.2274 270.6453 14808.66 11326.78 9337.134 8653.892 8058.417 7789.507 7624.406 7464.577 7248.09 7008.86 6771.214 6610.137 281.4898 311.0242 323.2914 328.7682 330.8688 332.1758 332.8287 333.1571 333.323 333.4071 333.4498 333.4714 290.9 430 401 484 350.9 220 289.9 297.9 327.8 363.9 310 278.9 2 Same 3 Same 0 Same ARI_1_ASE ARI_2_ASE EqualMeans_3_ASE EqualMeans_4_ASE EqualMeans_5_ASE ARI_6_ASE ARI_7_ASE ARI_8_ASE ARI_9_ASE EqualMeans_10_ASE EqualMeans_11_ASE EqualMeans_12_ASE